| Reference Frames |
Table of ContentsReference Frames Abstract Purpose Intended Audience Using Frames Frame Procedures in Icy Frame Transformation Procedures Frame Information Procedures Frames Supported in SPICE ICRF vs J2000 Kernels Needed For Computing Frame Transformations Creating a Frame Kernel Frame Classes Specifying a New Frame Guidelines for Frame Specification Selecting a Name Selecting a Frame ID Selecting the Class Selecting the Center Selecting a Class ID Frame IDs Reserved for Public Use Why have a Frame ID and a Class ID? Putting the Pieces Together Connecting an Object to its Body-fixed Frame The rest of the frame information Inertial Frames PCK Frames CK Frames SCLK and SPK ID codes TK Frames Defining a TK Frame Using a Matrix Defining a TK Frame Using Euler Angles Defining a TK Frame Using a SPICE-style Quaternion Gaining Flexibility via TK Frames Dynamic Frames Parameterized Dynamic Frame Families Notation Required Keywords for Parameterized Dynamic Frames Conditional Keywords for Parameterized Dynamic Frames Rotation State Freeze Epoch Two-Vector Frames Defining a Two-Vector Frame in a Frame Kernel Kernel Availability Specifying the Base Frame Specifying the Frame Family Specifying the Rotation state or Freeze Epoch Specifying the Angular Separation Tolerance Frame Axis Labels Vector Specifications Observer-Target Position Vectors Target Near point Vectors Observer-Target Velocity Vectors Constant Vectors Mean Equator and Equinox of Date Frames Defining a Mean Equator and Equinox of Date Frame in a Frame Kernel Specifying the Base Frame Specifying the Frame Family Specifying the Precession Model Specifying a Rotation State or Freeze Epoch True Equator and Equinox of Date Frames Defining a True Equator and Equinox of Date Frame in a Frame Kernel Specifying the Base Frame Specifying the Frame Family Specifying the Precession Model Specifying the Nutation Model Specifying a Rotation State or Freeze Epoch Mean Ecliptic and Equinox of Date Frames Defining a Mean Ecliptic and Equinox of Date Frame in a Frame Kernel Specifying the Base Frame Specifying the Frame Family Specifying the Precession Model Specifying the Mean Obliquity Model Specifying a Rotation State or Freeze Epoch Euler Frames Defining an Euler Frame in a Frame Kernel Specifying the Base Frame Specifying the Frame Family Specifying the Epoch Specifying the Euler Angles Product Frames Defining a Product Frame in a Frame Kernel Specifying the Base Frame Specifying the Frame Family Specifying the Factors Dynamic Frame Implementation Considerations Introduction Simulated Recursion The Need for Recursion in the Icy Frame Subsystem Implementation of Limited Simulated Recursion Limits on Recursion in Frame Definitions Frame Derivative Accuracy Degenerate Geometry Efficiency Concerns Switch Frames Specifying Switch Frames The Base Frame List Time Intervals Associated with Base Frames Binary Search Switch Frame Connections Switch Frame Buffering Appendix. ``Built in'' Inertial Reference Frames Complete List of ``Built in'' Inertial Reference Frames Inertial Reference Frame References Low Level Inertial Reference Frame Procedures Appendix. ``Built in'' PCK-Based IAU Body-Fixed Reference Frames Appendix. High Precision Earth Fixed Frames Appendix. Frame Identifiers Reserved for Earth Fixed Frames Appendix. Frame Definition Examples Inertial Frames PCK Frames CK Frames TK frames TK frame --- Alias TK frame --- Topographic TK frame --- Instrument Examples of Two-Vector Parameterized Dynamic Frames Geocentric Solar Ecliptic (GSE) Frame Geocentric Solar Magnetospheric (GSM) Frame Mercury Solar Equatorial (MSEQ) Frame Example: Nadir Frame for Mars Orbiting Spacecraft Example: Roll-Celestial Spacecraft Frame Examples of Mean Equator and Equinox of Date Frames Earth Mean Equator and Equinox of Date Frames Examples of True Equator and Equinox of Date Frames Example of a Mean Ecliptic and Equinox of Date Frame Example of an Euler Frame Examples of Product Frames IAU_EARTH Frame, Augmented with Nutation Model Dog-Leg Frame for Saturn Examples of Switch Frames Switch Frame Using Reconstructed and Predict CKs Switch Frame Using CK and Dynamic Frames Predicted Attitude Profile for Observation Planning Reference Frames
Abstract
Purpose
Intended Audience
This document assumes you have some familiarity with SPICE concepts and terminology. If you are new to the SPICE system, or just a bit rusty with it, you should consider reviewing ``An Overview of the SPICE System'' and ``An Introduction to SPICE.'' Using FramesFrame Procedures in Icy
Frame Transformation Procedures
The two user-level interface procedures that deal solely with frame transformations are cspice_sxform and cspice_pxform. cspice_sxform supports transformations of Cartesian state vectors (6 components) between reference frames while cspice_pxform supports transformations of Cartesian position vectors (3 components). cspice_pxform may be used when only position information is needed, or when the derivatives required for a state transformation are unavailable, for example when one frame is defined by a C-kernel that lacks angular velocity data. The calling sequences for these procedures are
cspice_sxform, from, to, et, xform
cspice_pxform, from, to, et, rotate
The output of cspice_sxform, `xform', is a 6 by 6 matrix used to
transform state vectors relative to a reference frame, the name of which
is specified by the `from' input argument, to states relative to another
reference frame, the name of which is specified by the `to' input
argument, at the epoch `et' (specified in seconds past J2000).
The output of cspice_pxform, `rotate', is a 3 by 3 transformation matrix equivalent to the upper left 3x3 block of `xform'. This matrix transforms position as opposed to state vectors. Frame Information Procedures
cspice_frmnam, frcode, frname cspice_namfrm, frname, frcode cspice_frinfo, frcode, cent, clss, clssid, found cspice_cidfrm, cent, frcode, frname, found cspice_cnmfrm, cname, frcode, frname, foundSee the section ``Specifying a New Frame'' below for more information on frame specification parameters. Frames Supported in SPICE
A number of names are automatically recognized by the frame subsystem because the definitions for these frames are ``built into'' Icy software. Among these frames are:
The types of frames defined in text kernels include:
cspice_furnsh, 'myframe.tf'
ICRF vs J2000
The rotational offset between the J2000 frame and the ICRS has magnitude of under 0.1 arcseconds. Certain JPL data products are referenced to the ICRF or later versions of it. These include, but are not limited to,
Modern spacecraft ephemerides and attitude data, other than those for Earth orbiters, are likely referenced to the ICRF. Users should consult documentation or data providers to verify this for data sets of interest. SPK and binary PCK files produced by NAIF from the data sources listed above are referenced to the same version of the ICRF as the corresponding data sources. For historical and backward compatibility reasons, these data products are labeled as being referenced to the J2000 frame. No transformation is required to convert state vectors or orientation data from the J2000 frame to the ICRF (or later version), if the vectors or orientation data are computed using SPICE kernels created from the data sources listed above. For example:
SPICE users who export kernel data to non-SPICE file formats may need to transform the data, depending on the frame to which the SPICE data are actually referenced (as opposed to the frame to which the kernel indicates the data are referenced), and depending on the desired output frame. Kernels Needed For Computing Frame Transformations
The ``built in'' inertial frames are the only frames the transformations between which can be computed without loading any SPICE kernels. Since the body-fixed frames are tied to the rotation of planets, satellites, asteroids, etc, the information about how the orientation of these frames is changing with respect to inertial frames is stored in SPICE PCK files. It is important to note that although the names of these frames are ``built in'' their relationship to inertial frames is not. This information must be ``loaded'' into the SPICE system from a PCK file. Without loading this information you cannot compute the transformation to or from a body-fixed frame. As the name suggests, the orientation of CK-based frames is computed using data provided in CK files and cannot be computed without loading these. In addition to the CKs, an SCLK kernel establishing time correlation for the on-board clock that is used to tag data in the CKs must be loaded to support time conversion between that clock and ephemeris time. Because the fixed offset frame definitions stored in text kernels provide all information needed to determine their orientation relative to the frame with respect to which they are defined, only the text kernel containing the definition need be loaded. Depending on the particular family to which a dynamic frame belongs, no additional data may be needed in order to compute its orientation, or one or more types of SPICE kernels, including SPKs, PCKs, CKs, and SCLK, may have to be loaded. Data required to compute orientation of switch frames may be any required to compute orientation of PCK, CK, or TK frames. Data for dynamic and switch base frames are not required because the orientation of a switch frame relative to base frames of those types is the identity. In practice, data sufficient to connect the orientation of a switch frame's base frames to other frames of interest are required by most applications. Creating a Frame Kernel
You will also need to understand the concept of a frame class. Frame Classes
Specifying a New Frame
Frame Name : 'WALDO'
Frame ID code : 1234567 (A number guaranteed to be suitable
for private use)
Frame Class : 3 (C-kernel)
Frame Center : -10001 (Waldo Spacecraft ID code)
Frame Class_id: -10000001 (ID code in C-kernel for Waldo)
The frame kernel that specifies this frame is given below:
\begindata
FRAME_WALDO = 1234567
FRAME_1234567_NAME = 'WALDO'
FRAME_1234567_CLASS = 3
FRAME_1234567_CENTER = -10001
FRAME_1234567_CLASS_ID = -10000001
\begintext
Guidelines for Frame SpecificationSelecting a Name
Selecting a Frame ID
If the class is CK, you may use the same ID as you use for the CLASS_ID. In the previous example, we selected the Frame ID to be 1234567. (Since our example frame above is of class 3, a CK frame, we would normally use the same number for the frame ID as we used for the class ID. However, in this example, we have chosen a different value to illustrate the connection between the frame ID and the variables needed to define the frame.) For TK frames, the frame and class IDs must be identical. For TK frames associated with an instrument, the instrument ID is used for both frame ID and class ID. For topocentric TK frames at tracking station sites, both frame ID and class ID are created by ``combining'' the ID of the body on which the station is located with the station number (for example frame and class ID 1399012 is used for ``DSS-12'', with the formula used to arrive at this ID being 1000000 + ``Earth ID''*1000 + ``station ID''.) For local level and surface fixed TK frames at a landing site, both frame ID and class ID are based on the ID of the lander (for example frame and class ID of -222999 would be the natural choice for the lander with ID -222.) If the frame is a PCK frame or a dynamic frame and you are working without consultation with NAIF, select an integer in the range from 1400000 to 2000000. Selecting the Class
Selecting the Center
Note that this center ID is used to look up the position of the frame origin when SPICE computes frame orientation adjusted for light time. Therefore, only centers for which supporting SPK data are expected to be available should be picked. It is usually an issue only for TK and CK frames associated with instruments because the positions of instruments are rarely available in SPKs. To get around the need to provide the instrument positions, it is appropriate to specify the ID of the spacecraft on which an instrument is mounted as the center of a TK or CK frame associated with it. Selecting a Class ID
If your frame is a PCK class frame the CLASS_ID is the ID code for the body for which rotation constants are provided in the text PCK file or the ID associated with the orientation data provided in the binary PCK file. If your frame is a CK class frame, the CLASS_ID is the ID code used in the C-kernel to describe the orientation of the spacecraft. If the frame is a TK frame, the class ID must match the frame ID. If the frame is a dynamic frame, the class ID must match the frame ID. If the frame is a switch frame, it is recommended that the class ID match the frame ID. Frame IDs Reserved for Public Use
Why have a Frame ID and a Class ID?
To support existing data products and allow extension of the SPICE system, NAIF needed to associate the old ID code with the new frame ID. The CLASS_ID fills this role. When the frame is identified, the ID code suitable for the frame class is located and passed onto the frame's class so that the initial portion of the frame transformation can be carried out. Putting the Pieces Together
FRAME_<name> = <ID code> FRAME_<ID code>_NAME = '<name>' FRAME_<ID code>_CLASS = <class> FRAME_<ID code>_CLASS_ID = <classid> FRAME_<ID code>_CENTER = <center>The example we used for the frame 'WALDO' illustrates this.
\begindata
FRAME_WALDO = 1234567
FRAME_1234567_NAME = 'WALDO'
FRAME_1234567_CLASS = 3
FRAME_1234567_CENTER = -10001
FRAME_1234567_CLASS_ID = -10000001
\begintext
Once you've completed the frame specification you tell the SPICE system
about the frame by ``loading'' the frame kernel that contains it. As
with all text kernels, you load it via the routine cspice_furnsh. For
example if the frame kernel containing your frame specification is
contained in the file ``myframe.tf'' you load the kernel via the call
cspice_furnsh, 'myframe.tf'
Connecting an Object to its Body-fixed Frame
OBJECT_<name or spk_id>_FRAME = '<frame name>'or
OBJECT_<name or spk_id>_FRAME = <frame ID code>You may use the ID codes for either the object, the frame or both. As example, four of the following assignments could serve to connect the Earth with the 'ITRF93' frame.
OBJECT_399_FRAME = 13000 OBJECT_399_FRAME = 'ITRF93' OBJECT_EARTH_FRAME = 13000 OBJECT_EARTH_FRAME = 'ITRF93'Note: if you use the name of either the object or frame, you must use upper case letters. Of these four means of specifying an object's body-fixed frame the second (OBJECT_399_FRAME = 'ITRF93') is the most robust. For the sun, the planets and their satellites the frame subsystem maintains a default connection between the object and its body-fixed frame ``built into'' SPICE. The complete list of ``built in'' body-fixed frames is provided in the ``built in PCK-Based IAU Body-Fixed Reference Frames'' appendix of this document. The rest of the frame information
Inertial Frames
It is possible to create aliases for built-in inertial frames. For example you might define EME2000 as another name for the J2000 frame. See the appendix containing frame definition examples for information on how to create a frame alias using a TK frame. PCK Frames
CK Frames
SCLK and SPK ID codes
CK_<ck_ID code>_SCLK = <ID code of SCLK> CK_<ck_ID code>_SPK = <SPK ID code>These variables are normally placed in either the SCLK kernel or in the frame specification kernel (FK). To illustrate how you would create a C-kernel frame, we shall suppose that we have a C-kernel for structure -100001 aboard the fictional spacecraft ``Waldo'' which has ID code -1001. Moreover we shall assume that the clock ID appropriate for this structure is -1002. Below is a frame specification together with the CK_..._SCLK and CK_..._SPK variable definitions for the 'WALDO' frame.
\begindata
FRAME_WALDO = -100001
FRAME_-100001_NAME = 'WALDO'
FRAME_-100001_CLASS = 3
FRAME_-100001_CLASS_ID = -100001
FRAME_-100001_CENTER = -1001
CK_-100001_SCLK = -1002
CK_-100001_SPK = -1001
\begintext
TK Frames
FRAME_<name> = <ID code> FRAME_<ID code>_NAME = '<name>' FRAME_<ID code>_CLASS = 4 FRAME_<ID code>_CLASS_ID = <ID code> FRAME_<ID code>_CENTER = <center>You need to supply information that indicates the frame, RELATIVE, from which the TK frame is offset. It is done using this kernel pool variable:
TKFRAME_<frame>_RELATIVE = '<name of relative frame>'where `frame' is the ID code or name you used in the frame specification. Because the rotation from the TK frame to the RELATIVE frame is fixed (time invariant) it can be specified in the FK along with the frame specification information described above. This rotation data can be provided in any of three ways:
V_relative = M * V_tkframe
TKFRAME_<frame>_SPEC.To use a matrix to define the rotation, use the assignment:
TKFRAME_<frame>_SPEC = 'MATRIX'To define the rotation via three Euler angles, use the assignment:
TKFRAME_<frame>_SPEC = 'ANGLES'To define the rotation via a SPICE-style quaternion, use the assignment:
TKFRAME_<frame>_SPEC = 'QUATERNION'Depending upon the value of the `SPEC' variable, you need to supply one of the following sets of kernel pool variables. Defining a TK Frame Using a Matrix
TKFRAME_<frame>_MATRIX = ( matrix_value[0,0],
matrix_value[1,0],
matrix_value[2,0],
matrix_value[0,1],
matrix_value[1,1],
matrix_value[2,1],
matrix_value[0,2],
matrix_value[1,2],
matrix_value[2,2] )
For example, if the matrix defining your TK frame is
0.4 -0.6 0.0 0.6 0.4 0.0 0.0 0.0 1.0and the ID code you've selected for the frame is 1234567, then you would supply the following information in a text kernel.
TKFRAME_1234567_SPEC = 'MATRIX'
TKFRAME_1234567_MATRIX = ( 0.4
0.6
0.0
-0.6
0.4
0.0
0.0
0.0
1.0 )
Defining a TK Frame Using Euler Angles
TKFRAME_<frame>_ANGLES = ( angle_1, angle_2, angle_3 ) TKFRAME_<frame>_AXES = ( axis_1, axis_2, axis_3 ) TKFRAME_<frame>_UNITS = 'units_of_angles'The units must be from the list given above. The axes must be chosen from the set of integers 1,2,3 where 1 stands for the x-axis, 2 for the y-axis, and 3 for the z-axis. If M is the matrix that converts vectors relative to the TK frame to the RELATIVE frame by left multiplication, then the angles and axes must satisfy the following relationship:
M = [angle_1] [angle_2] [angle_3]
axis_1 axis_2 axis_3
where the symbol
[ A ]
i
stands for a rotation by the angle A about the i'th axis.
+- -+ | 1 0 0 | | 0 cos A sin A | = [ A ] | 0 -sin A cos A | 1 +- -+ +- -+ | cos A 0 -sin A | | 0 1 0 | = [ A ] | sin A 0 cos A | 2 +- -+ +- -+ | cos A sin A 0 | | -sin A cos A 0 | = [ A ] | 0 0 1 | 3 +- -+This method of definition is particularly well suited for defining topocentric frames on the surface of the Earth. For example, suppose you have an SPK (ephemeris) file that specifies the location of some surface point on the Earth, and that the SPK ID code of this point is 399100. Moreover suppose you have the geodetic co-latitude (COLAT) and longitude (LONG) measured in degrees for this point. (Note that the co-latitude is the complement of latitude: latitude + co-latitude = 90 degrees.) Given this information we can easily define a topocentric reference frame at the point such that the x-axis points north along the local meridian, the y-axis points west along the local latitude and the z-axis points up from the reference spheroid. The transformation from Earth body-fixed frame to topocentric frame is given by
BF2TP = [180] [COLAT] [LONG]
3 2 3
Consequently the transformation from the topocentric frame to the
body-fixed frame is given by
M = TP2BF = [-LONG] [-COLAT] [180]
3 2 3
Let 1234567 be the ID code for the topocentric frame; let the name of
this frame be 'MYTOPO'; and define this relative to the IAU frame for
the Earth (one of the ``built in'' frames). The topocentric frame at the
ephemeris point 399100 is specified as shown below:
\begindata
FRAME_MYTOPO = 1234567
FRAME_1234567_NAME = 'MYTOPO'
FRAME_1234567_CLASS = 4
FRAME_1234567_CLASS_ID = 1234567
FRAME_1234567_CENTER = 399100
TKFRAME_1234567_SPEC = 'ANGLES'
TKFRAME_1234567_RELATIVE = 'IAU_EARTH'
TKFRAME_1234567_ANGLES = ( <-long>, <-colat>, 180 )
TKFRAME_1234567_AXES = ( 3, 2, 3 )
TKFRAME_1234567_UNITS = 'DEGREES'
\begintext
As we'll see a bit later, we can make a more flexible definition for
this topocentric frame.
Defining a TK Frame Using a SPICE-style Quaternion
TKFRAME_<frame>_Q = ( q_0, q_1, q_2, q_3 )where component zero is the so-called ``real'' component of the quaternion (the ``cosine'' component of the quaternion). The last 3 components (components 1 through 3) are the ``axis'' components of the quaternion -- the i, j, and k components respectively of the quaternion. The quaternion must be a unit quaternion.
2 2 2 2
(q_0) + (q_1) + (q_2) + (q_3) = 1
A more detailed discussion of quaternions is available in the reference
document ``Rotations Required Reading'' (rotation.req), and in a
``Quaternions White Paper'' available from NAIF.
Gaining Flexibility via TK Frames
\begindata
FRAME_MOONFIXED = 3010000
FRAME_3010000_NAME = 'MOONFIXED'
FRAME_3010000_CLASS = 4
FRAME_3010000_CLASS_ID = 3010000
FRAME_3010000_CENTER = 301
TKFRAME_3010000_SPEC = 'MATRIX'
TKFRAME_3010000_RELATIVE = '<name of base frame>'
TKFRAME_3010000_MATRIX = ( 1,
0,
0,
0,
1,
0,
0,
0,
1 )
\begintext
By editing this definition you can make the MOONFIXED frame be the IAU
MOON frame or some other model if one is available. Or you can create
several such definitions and, at run-time, load the file that best fits
your current environment.
Using this indirect method of defining the various frames for which more than one orientation model may be available, you can avoid limiting how various kernels can be used. Dynamic Frames
A ``parameterized dynamic frame'' is a dynamic frame defined by a formula implemented in Icy code and having user-selectable parameters set via a frame kernel. The formula defining a dynamic frame may rely on data from other SPICE kernels, for example state vectors provided by SPK files or rotation matrices from C-kernels or PCK files. An example of a parameterized dynamic frame is a nadir-pointing reference frame for a spacecraft orbiting a planet, where the spacecraft's nadir direction and velocity vector define the frame. Using a frame kernel, a Icy user may specify the planet and spacecraft, the relationship between the nadir and velocity vectors and the frame's axes, and a small set of additional parameters required to define the frame. Currently parameterized dynamic frames are the only type of dynamic frame supported by Icy. Other types of dynamic frames, such as frames defined by complete formulas (as opposed to parameters) provided in frame kernels, may be implemented in future versions of Icy. Below we'll discuss the various types of supported dynamic frames, how to create frame kernels that define dynamic frames, and dynamic frame implementation considerations. The appendix ``Frame Definition Examples'' contains frame definition templates for a variety of popular dynamic frames. Parameterized Dynamic Frame Families
Notation
C = A x BDouble vertical bars bracketing the name of a vector indicate the norm of the vector:
||A||Throughout this discussion we'll use text enclosed in angle brackets to indicate values to be filled in by the creator of a frame kernel. Examples are:
Token Replacement Value
------------- -----------------------------------------
<vec_ID> 'PRI' or 'SEC' [See discussion of
two-vector frames below.]
<frame_name> SPICE frame name, .e.g. 'J2000'
<frame_ID> Integer frame ID code
<observer_ID> NAIF integer ID for the observing body
<aberration correction> String indicating aberration correction,
e.g.: 'NONE', 'LT', 'XLT', 'LT+S'
Required Keywords for Parameterized Dynamic Frames
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = <center_ID> FRAME_<frame_ID>_RELATIVE = <base_frame_name> FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = <frame_family>These first five of the assignments are common to all Icy frame definitions; the class code 5 indicates that the frame is dynamic. See the section ``Guidelines for Frame Specification'' in the chapter ``Creating a Frame Kernel'' above for a detailed discussion of these assignments. The sixth assignment (for keyword FRAME_<frame_ID>_RELATIVE) is the ``base frame'' specification; this indicates the frame the transformation defined by the frame kernel ``maps to'': starting with an epoch ET and a state vector S specified relative to the defined frame
<frame name>the frame definition determines the 6x6 state transformation matrix XFORM such that the product
XFORM * Syields the equivalent state specified relative to the base frame at ET. The seventh assignment (for keyword FRAME_<frame_ID>_DEF_STYLE) is used to simplify future implementation of other dynamic frame definition styles. Only the value
'PARAMETERIZED'is currently supported. The last assignment indicates the frame family. The possible values are
'TWO-VECTOR' 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE' 'EULER'Additional, required frame kernel assignments are a function of the family to which a dynamic frame belongs. These are discussed below. Conditional Keywords for Parameterized Dynamic FramesRotation State
When a parameterized dynamic frame is specified as ``inertial,'' the derivative with respect to time of the transformation between the frame and any inertial frame, for example the J2000 frame, is zero. The rotation between the frame and any inertial frame is still treated as time-dependent. For such a frame F, the call
cspice_sxform, 'F', 'J2000', t, xformyields a 6x6 state transformation matrix `xform' having the structure
+-----+-----+ | R(t)| 0 | +-----+-----+ | 0 | R(t)| +-----+-----+where R(t) is the 3x3 rotation matrix that transforms vectors from frame F to the J2000 frame at time `t'. By contrast, when the rotation state of F is ``rotating,'' `xform' has the structure
+-----+-----+ | R(t)| 0 | +-----+-----+ |dR/dt| R(t)| +-----+-----+So, when the rotation state of frame F is ``inertial,'' velocities are transformed from frame F to J2000 by left-multiplication by R(t); the time derivative of the rotation from F to J2000 is simply ignored. Normally the inertial rotation state makes sense only for slowly rotating frames such as the earth mean equator and equinox of date frame. A parameterized dynamic frame's rotation state is specified via the assignment
FRAME_<frame_ID>_ROTATION_STATE = <state>where
<state>is one of
'ROTATING' 'INERTIAL'For frames belonging to the parameterized dynamic frame families
'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE'either the rotation state must be specified, or the frame must be frozen (see ``Frozen Frames'' below). For two-vector and Euler frames, the rotation state specification is optional; these frames are considered to be rotating by default. When the rotation state of a parameterized frame is specified, the frame cannot be frozen; these options are mutually exclusive. Freeze Epoch
A frozen frame whose base frame is time-varying is still time-varying: it is the relationship between the frozen frame and the base frame that is time-independent. A frame is declared frozen by specifying a ``freeze epoch.'' This is done via the assignment:
FRAME_<frame_ID>_FREEZE_EPOCH = <time_spec>where
<time_spec>is a TDB calendar date whose format conforms to the SPICE text kernel date format specification. These dates
@
@YYYY-MON-DD/HR:MN.SEC.###Literal examples include
@7-MAR-2005 @March-7-2005-3:10:39.221 @2005-MAR-07/3:10:39.221Note that unlike time strings supported by the Icy procedure cspice_str2et, time system tokens such as
UTC TDT TDBare not supported; times are always assumed to be TDB. For frames belonging to the parameterized dynamic frame families
'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE'either the frame must be frozen or the rotation state must be specified, (see ``Rotation State'' above). For two-vector and Euler frames, the freeze epoch specification is optional; these frames are considered to be time-varying relative to their base frames by default. When a parameterized frame is frozen, the rotation state of the frame cannot be specified; these options are mutually exclusive. Two-Vector Frames
In a two-vector frame definition, one defining vector is parallel to a specified axis of the reference frame; this vector is called the ``primary vector.'' The other vector, called the ``secondary vector,'' defines another axis: the component of the secondary vector orthogonal to the primary vector is parallel to a specified axis of the reference frame. The secondary vector itself need not be, and typically is not, aligned with an axis of the defined frame. Below, we'll call the primary and secondary defining vectors PRI and SEC, and we'll name the axes of the right-handed frame X, Y, and Z. The unit +Z vector is the cross product of the unit +X and +Y vector. In a two-vector frame definition, the vectors PRI and SEC are specified geometrically; for example, PRI could be the position of the earth relative to a spacecraft, and SEC could be defined by the right ascension and declination of a given star in a specified reference frame. In a frame kernel, the vectors PRI and SEC are associated with two members of the set of unit vectors
{ X, -X, Y, -Y, Z, -Z }
An example: in this case PRI is associated with -Z and SEC is associated
with +X. SEC itself is not parallel to the X axis, but the component of
SEC orthogonal to PRI points in the +X direction.
The diagram below shows the relationship between PRI, SEC, X, Y, and Z:
Component of SEC orthogonal to PRI
|
| ^
v |
<-----+--+
\ | |
\ +--+
\ |
SEC \ | +Z = - PRI / ||PRI||
\ |
\ |
\ +--+
\| |
+X = Y x Z <---------+---+--+
/ /|
+---/ |
/| /
/ |/|
/ + | -Z = PRI / ||PRI||
/ |
/ |
v v PRI
Z x SEC
+Y = -----------
||Z x SEC||
= Z x X
By defining PRI and SEC we can create a concrete frame definition.
Continuing the above example, we can define a nadir-pointing frame for
the Mars Global Surveyor (MGS) spacecraft as follows:
PRI = Vector from MGS to nearest point on Mars reference
ellipsoid
Z = -PRI / ||PRI||
SEC = Inertially referenced velocity of MGS relative to Mars
Y = Z x SEC / ||Z x SEC||
X = Y x Z
For this nadir-pointing frame, -Z is the nadir direction, X points
roughly in the direction of the inertially referenced spacecraft
velocity, and Y is aligned with the orbital angular velocity vector.
By converting the above definition into the frame kernel ``keyword=value'' format, we can make the definition usable by the Icy system. Above, for brevity, we've glossed over a few aspects of the vector definitions. Below we'll discuss in detail all of the elements of two-vector frame specifications. Defining a Two-Vector Frame in a Frame KernelKernel Availability
We'll also call a frame transformation between frames F1 and F2 ``computable'' if both frames F1 and F2 are computable and kernels have been loaded sufficient to enable computation of the transformation between F1 and F2. For example, the transformation between the J2000 and IAU_TITAN frames is computable once a PCK containing rotational elements for TITAN has been loaded. Specifying the Base Frame
For a two-vector frame, the base frame may be any frame F_BASE such that the transformation between F_BASE and the J2000 reference frame is computable at the time the two-vector frame definition is referenced. Normally for two-vector frames the base frame should be set to 'J2000'; this choice yields optimal run-time efficiency. The assignment is made as follows.
FRAME_<frame_ID>_RELATIVE = 'J2000'Base frame specifications are part of the two-vector frame definition because the base frame can be used to control how Icy chains together two-vector frames with other frames. However, from a mathematical point of view, two-vector frames are fully defined without reference to a base frame. For example, suppose the two-vector frame F1 is defined by the earth-moon position vector and the earth-sun position vector, and the base frame for F1 is IAU_EARTH. Suppose that the two-vector frame F2 is defined by the same vectors and that the base frame of F2 is J2000. Then, ignoring small round-off errors, the transformation between F1 and F2 is the identity transformation. Base frames should not be confused with other frames occurring in two-vector frame definitions: constant vectors and velocity vectors have associated frames which are also specified by keyword assignments. See the discussion below under the heading ``Constant Vectors'' and ``Velocity Vectors'' for details. Specifying the Frame Family
FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR'Further assignments (discussed below) define the primary and secondary vectors and relate these vectors to the frame's axes. Specifying the Rotation state or Freeze Epoch
Specifying the Angular Separation Tolerance
FRAME_<frame_ID>_ANGLE_SEP_TOL = <tolerance>where <tolerance> is the separation limit in radians. If the angular separation of the defining vectors differs from zero or pi radians by less than the specified tolerance, an error will be signaled at run time. When a two-vector frame definition omits specification of an angular separation tolerance, Icy uses a default value of one milliradian. Frame Axis Labels
FRAME_<frame_ID>_PRI_AXIS = <label>Here
<label>may be any of
{ 'X', '-X', 'Y', '-Y', 'Z', '-Z' }
Blanks and case in the label are not significant. Unsigned axis
designations are treated as positive; optionally '+' signs may be used
to prefix positive axis designations. The primary vector is aligned with
the indicated axis and has the sense indicated by the implied or
explicit sign.
The secondary defining vector is associated with a frame axis via the assignment
FRAME_<frame_ID>_SEC_AXIS = <label>where the axis labels are as above. The assignment means that the component of the secondary vector orthogonal to the primary vector is aligned with the indicated axis and has the sense indicated by the implied or explicit sign. Vector Specifications
All keywords comprising the primary vector definition start with the prefix
FRAME_<frame_ID>_PRI_All keywords for the second defining vector are prefixed by
FRAME_<frame_ID>_SEC_Here <frame_ID> is the integer ID code for the frame being defined. Both the primary and secondary vectors are specified using the sets of keywords described below. Observer-Target Position Vectors
The observer and target are specified by name or ID code. The aberration correction may be any value accepted by cspice_spkezr. The frame kernel assignments used to define an observer-target position vector are:
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or ID code> FRAME_<frame_ID>_<vec_ID>_TARGET = <target name or ID code> FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correction>where <vec_ID> may be either PRI or SEC, and <frame_ID> is the ID code of the frame established by the generic assignments described above. In order for a two-vector frame using a position vector as part of its definition to be computable, kernel data must be loaded that enable computation of the specified position vector with respect to the J2000 frame. For an example of a two-vector frame definition using an observer-target position vector, see the subsection titled ``Geocentric Solar Ecliptic (GSE) Frame'' in the appendix ``Frame Definition Examples.'' Target Near point Vectors
Target near point vectors are defined by an observer, a target, an aberration correction, a frame, and an epoch. As with position vectors, the frame and epoch are not specified in the frame kernel. The observer and target are specified by name or ID code. Aberration corrections may be any supported by the Icy procedure cspice_subpt. Light time corrections are applied both to the observer- target center vector and to the rotation of the target body. The stellar aberration correction, if specified, is applied to the observer-target center vector. The frame kernel assignments used to define a target near point position vector are:
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'TARGET_NEAR_POINT' FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or ID code> FRAME_<frame_ID>_<vec_ID>_TARGET = <target name or ID code> FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correction>In order for a two-vector frame using a target near point vector as part of its definition to be computable, kernel data must be loaded that enable computation of the target near point vector with respect to the J2000 frame. For an example of a two-vector frame definition using a target near point vector, see the subsection titled ``Nadir Frame for Mars Orbiting Spacecraft'' in the appendix ``Frame Definition Examples.'' Observer-Target Velocity Vectors
When the velocity frame is non-inertial and aberration corrections are used, the epoch at which the velocity frame is evaluated will be adjusted by the one-way light time between the observer and the frame's center---just as is done by cspice_spkezr (see the header of that procedure for details). The reason the velocity frame specification is crucial is that, (unlike rotations) state transformations between non-inertial frames don't preserve geometric properties of velocity vectors. Example: compare the specific angular momentum vector of a geosynchronous satellite (obtained by taking the cross product of the satellite's geocentric position and velocity vectors) in both the J2000 frame and in the earth body-fixed frame. In the latter frame, the specific angular momentum is zero. A valid two-vector frame could be defined using the satellite's position and velocity in the J2000 frame, while using the position and velocity in the earth body-fixed frame gives rise to a degenerate case for which the two-vector frame is undefined. The observer and target defining the velocity vector are specified by name or ID code. The aberration correction may be any value accepted by cspice_spkezr. The velocity frame may be any computable by Icy, including a dynamic frame, as long as the transformation between the velocity frame and the J2000 frame doesn't require multiple levels of simulated recursion (see the discussion of recursion in the chapter ``Dynamic Frame Implementation Considerations'' below for details). The frame kernel assignments used to define an observer-target velocity vector are:
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY' FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or ID code> FRAME_<frame_ID>_<vec_ID>_TARGET = <target name or ID code> FRAME_<frame_ID>_<vec_ID>_FRAME = <frame_name> FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correction>In order for a two-vector frame using a velocity vector as part of its definition to be computable, kernel data must be loaded that enable computation of the velocity vector with respect to both the velocity frame and the J2000 frame. For an example of a two-vector frame definition using an observer-target velocity vector, see the subsection titled ``Geocentric Solar Ecliptic (GSE) Frame'' in the appendix ``Frame Definition Examples.'' Constant Vectors
The coordinates of a constant vector may be specified in any of the rectangular, latitudinal, or RA/DEC (right ascension and declination) systems. If the coordinates are angular, the associated angular units must be specified; any angular units supported by the Icy procedure cspice_convrt may be used. All constant vectors require the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_<vec_ID>_SPEC = <coordinate_system> FRAME_<frame_ID>_<vec_ID>_FRAME = <frame_name>where <coordinate_system> is one of
'RECTANGULAR' 'LATITUDINAL' 'RA/DEC'and the frame is any computable by Icy, including a dynamic frame, as long as the transformation between the constant vector's frame and the J2000 frame doesn't require multiple levels of simulated recursion (see the discussion of recursion in the chapter ``Dynamic Frame Implementation Considerations'' below for details). When the coordinate system is rectangular, the vector is specified by the frame kernel assignment
FRAME_<frame_ID>_<vec_ID>_SPEC = 'RECTANGULAR'
FRAME_<frame_ID>_<vec_ID>_VECTOR = ( <X component>,
<Y component>,
<Z component> )
When the coordinate system is latitudinal, the vector is specified by
the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_SPEC = 'LATITUDINAL' FRAME_<frame_ID>_<vec_ID>_UNITS = <angular_units> FRAME_<frame_ID>_<vec_ID>_LONGITUDE = <longitude> FRAME_<frame_ID>_<vec_ID>_LATITUDE = <latitude>where <angular_units> designates one of the units supported by the Icy procedure cspice_convrt. The set of supported units includes
'RADIANS' 'DEGREES' 'ARCSECONDS'When the coordinate system is RA/DEC, the vector is specified by the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_SPEC = 'RA/DEC' FRAME_<frame_ID>_<vec_ID>_UNITS = <angular_units> FRAME_<frame_ID>_<vec_ID>_RA = <RA> FRAME_<frame_ID>_<vec_ID>_DEC = <DEC>where <angular_units> are as described above. Aberration corrections are optional for constant vectors. The set of available corrections is unique to this application: either light time correction or stellar aberration correction may be applied, but both cannot be applied together. Light time corrections adjust the orientation of the constant vector's frame for the one-way light time between the center of the frame and a specified observer. The application to the frame of light time correction is identical to that performed by the Icy procedure cspice_spkezr when it is asked to compute a light-time corrected state relative to a non-inertial reference frame. Supported light time corrections are any of those supported by cspice_spkezr that don't include stellar aberration correction. The user may also correct the constant vector for stellar aberration; this correction is a function of the constant vector and the velocity of an observer relative to the solar system barycenter. A typical application would be to correct an inertially referenced star direction vector for the stellar aberration induced by motion of an observing spacecraft. The supported stellar aberration corrections are
'S' {correct for stellar aberration, reception case}
'XS' {correct for stellar aberration, transmission case}
In the application above, one would correct the apparent observer-star
direction by selecting the 'S' option. See the discussion in the header
of the Icy procedure cspice_spkezr for a description of the
``reception'' and ``transmission'' aberration correction cases.
When aberration corrections are desired, the observer and the correction are specified by the frame kernel assignments
FRAME_<frame_ID>_<vec_ID>_OBSERVER = <observer name or ID code> FRAME_<frame_ID>_<vec_ID>_ABCORR = <aberration correction>In order for a two-vector frame using a constant vector as part of its definition to be computable, kernel data must be loaded that enable computation of the specified vector with respect to both the constant vector's frame and the J2000 frame. For examples of two-vector frame definitions using constant vectors, see the subsections titled ``Geocentric Solar Magnetospheric (GSM) Frame'' and ``Mercury Solar Equatorial (MSEQ) Frame'' in the appendix ``Frame Definition Examples.'' Mean Equator and Equinox of Date Frames
The mathematical model for a mean equator and equinox of date frame is typically called a ``precession model''; Icy adopts this usage. The Icy frame subsystem supports mean equator and equinox of date frames via precession models built into Icy. In principle, for any body, a frame kernel definition for a mean equator and equinox of date frame identifies which precession model to use for that body. Currently Icy supports only one precession model: the 1976 IAU precession model for the earth. Defining a Mean Equator and Equinox of Date Frame in a Frame KernelSpecifying the Base Frame
FRAME_<frame_ID>_RELATIVE = 'J2000' Specifying the Frame Family
FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' Specifying the Precession Model
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' Specifying a Rotation State or Freeze Epoch
Users can instruct the Icy frame subsystem to treat a mean equator and equinox of date frame as either inertial or rotating by making a ``rotation state'' assignment. Users can also direct the frame subsystem to treat a mean equator and equinox of date frame as though it were ``frozen'' at a specified epoch. See the section above titled ``Conditional Keywords for Parameterized Dynamic Frames'' for instructions on how to make these assignments. Definitions of mean equator and equinox of date frames require either, but not both, the rotation state or a freeze epoch to be specified. For examples of Mean Equator and Equinox of Date frame definitions, see the subsection titled ``Earth Mean Equator and Equinox of Date Frames'' in the appendix ``Frame Definition Examples.'' True Equator and Equinox of Date Frames
Defining a True Equator and Equinox of Date Frame in a Frame Kernel
Specifying the Base Frame
FRAME_<frame_ID>_RELATIVE = 'J2000' Specifying the Frame Family
FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' Specifying the Precession Model
The 1976 IAU precession model is ``selected'' via the assignment:
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' Specifying the Nutation Model
FRAME_<frame_ID>_NUT_MODEL = <nutation_model>Currently the only available nutation model is the 1980 IAU nutation model for the earth. An assignment specifying this model has the form:
FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980' Specifying a Rotation State or Freeze Epoch
Users can instruct the Icy frame subsystem to treat a true equator and equinox of date frame as either inertial or rotating by making a ``rotation state'' assignment. Users can also direct the frame subsystem to treat a true equator and equinox of date frame as though it were ``frozen'' at a specified epoch. See the section above titled ``Conditional Keywords for Parameterized Dynamic Frames'' for instructions on how to make these assignments. Definitions of true equator and equinox of date frames require either, but not both, the rotation state or a freeze epoch to be specified. For examples of True Equator and Equinox of Date frame definitions, see the subsection titled ``Earth True Equator and Equinox of Date Frames'' in the appendix ``Frame Definition Examples.'' Mean Ecliptic and Equinox of Date Frames
The term ``mean equator'' indicates that orientation of a body's equatorial plane is modeled accounting for precession. The ``mean equinox'' is the intersection of the body's mean orbital plane with the mean equatorial plane. The X-axis of such a frame is aligned with the cross product of the north-pointing vectors normal to the body's mean equator and mean orbital plane of date. The Z-axis is aligned with the second of these normal vectors. The Y axis is the cross product of the Z and X axes. The term ``of date'' means that these axes are evaluated at a specified epoch. Defining a Mean Ecliptic and Equinox of Date Frame in a Frame Kernel
Specifying the Base Frame
FRAME_<frame_ID>_RELATIVE = 'J2000' Specifying the Frame Family
FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE' Specifying the Precession Model
The 1976 IAU precession model is ``selected'' via the assignment:
FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' Specifying the Mean Obliquity Model
FRAME_<frame_ID>_OBLIQ_MODEL = <obliquity_model>Currently the only available mean obliquity model is the 1980 IAU obliquity model for the earth. An assignment specifying this model has the form:
FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980' Specifying a Rotation State or Freeze Epoch
Users can instruct the Icy frame subsystem to treat a mean ecliptic and equinox of date frame as either inertial or rotating by making a ``rotation state'' assignment. Users can also direct the frame subsystem to treat a mean ecliptic and equinox of date frame as though it were ``frozen'' at a specified epoch. See the section above titled ``Conditional Keywords for Parameterized Dynamic Frames'' for instructions on how to make these assignments. Definitions of mean ecliptic and equinox of date frames require either, but not both, the rotation state or a freeze epoch to be specified. For examples of Mean Ecliptic and Equinox of Date frame definitions, see the subsection titled ``Earth Mean Ecliptic and Equinox of Date Frames'' in the appendix ``Frame Definition Examples.'' Euler Frames
The rotation defined by the Euler angles maps position vectors via left multiplication from the defined Euler reference frame to the base frame:
V = r(t) * V
base_frame Euler_frame
This rotation can be considered to be a time-dependent matrix
r(t)where r(t) represents the composition of the rotations defined by the input angle-axis pairs. Naming the axis indices and angles of the Euler angle sequence
axindx_i, angle_i, i = 1, 2, 3r(t) is
r(t) = [ angle_1(t) ] [ angle_2(t) ] [ angle_3(t) ]
axindx_1 axindx_2 axindx_3
The axis indices axindx_i, for i = 1, 2, 3, are in the set { 1, 2, 3 };
axindx_2 cannot equal axindx_1 or axindx_3. For example, we could have
axindx_1 = 3 axindx_2 = 1 axindx_3 = 3Here the notation
[ A ]
j
stands for a frame rotation by the angle A radians about the jth axis of
a right-handed frame, where we assign the axes {X, Y, Z} the indices {1,
2, 3} respectively:
+- -+ | 1 0 0 | | 0 cos A sin A | = [ A ] | 0 -sin A cos A | 1 +- -+ +- -+ | cos A 0 -sin A | | 0 1 0 | = [ A ] | sin A 0 cos A | 2 +- -+ +- -+ | cos A sin A 0 | | -sin A cos A 0 | = [ A ] | 0 0 1 | 3 +- -+The base frame can be constructed from the Euler frame via a sequence of Euler angle rotations as follows:
The rotation angles are defined as follows: letting t0 represent the reference epoch, and letting
c , i = 1, 2, 3; j = 0, ... , ni
i,j
be the polynomial coefficients for the ith angle, we have
n1
angle_1(t) = c + c * (t-t0) + ... + c * (t-t0)
1,0 1,1 1,n1
n2
angle_2(t) = c + c * (t-t0) + ... + c * (t-t0)
2,0 2,1 2,n2
n3
angle_3(t) = c + c * (t-t0) + ... + c * (t-t0)
3,0 3,1 3,n3
See the Rotation Required Reading, rotation.req, or the header of the
Icy procedure cspice_eul2m for details concerning definition of
rotations via Euler angles. Note however that the referenced document
and source code use a different convention for labeling Euler angles and
their rotation axes: here the elements of the rotation sequence are
numbered left to right; in those documents the order is that in which
rotations are performed, namely right to left.
Defining an Euler Frame in a Frame KernelSpecifying the Base Frame
FRAME_<frame_ID>_RELATIVE = '<frame_name>' Specifying the Frame Family
FRAME_<frame_ID>_FAMILY = 'EULER' Specifying the Epoch
FRAME_<frame_ID>_EPOCH = @YYYY-MON-DD/HR:MN.SEC.###A concrete example is:
FRAME_<frame_ID>_EPOCH = @2000-JAN-1/12:00:00.000The calendar time string is assumed to represent a TDB epoch. See the discussion in the section ``Freeze Epoch'' above or the Kernel Required Reading, kernel.req, for further information. Specifying the Euler Angles
FRAME_<frame_ID>_AXES = ( <index of axis 1>
<index of axis 2>
<index of axis 3> )
The axis indices must be taken from the set
{ 1, 2, 3 }
and the middle value must differ from its neighbors. The first integer
listed is the axis index for angle 1, the second for angle 2, and the
last for angle 3, where the role of the angles is as shown in the
equation for r(t) above.
Let n1, n2, and n3 represent the maximum degrees of the polynomials for angles 1, 2, and 3 respectively. Then the polynomial coefficients are defined by the assignments
FRAME_<frame_ID>_ANGLE_1_COEFFS = ( <order 0 coefficient>
<order 1 coefficient>
...
<order n1 coefficient> )
FRAME_<frame_ID>_ANGLE_2_COEFFS = ( <order 0 coefficient>
<order 1 coefficient>
...
<order n2 coefficient> )
FRAME_<frame_ID>_ANGLE_3_COEFFS = ( <order 0 coefficient>
<order 1 coefficient>
...
<order n3 coefficient> )
Angular units are specified by the frame kernel assignment
FRAME_<frame_ID>_UNITS = <angular_units>where <angular_units> designates one of the units supported by the Icy procedure cspice_convrt. The set of supported units includes
'RADIANS' 'DEGREES' 'ARCSECONDS'For an example of an Euler frame definition, see the subsection titled ``Euler Frames'' in the appendix ``Frame Definition Examples.'' Product Frames
Using the notation
B
T
A
to indicate the transformation from frame A to frame B, and letting the
names
PRODUCT BASEdenote a product frame and a ``base'' frame relative to which the orientation of the product frame is defined, the transformation from the base frame to the product frame is defined by a product of one or more frame transformation ``factors'' consisting of transformations from a given ``from'' frame to a given ``to'' frame:
PRODUCT TO_1 TO_2 TO_N-1 TO_N
T = T * T * ... * T * T
BASE FROM_1 FROM_2 FROM_N-1 FROM_N
If the vector
v
BASE
is expressed relative to the base frame, then applying a product frame
transformation to the vector expresses the vector relative to the
product frame:
PRODUCT
v = T * v
PRODUCT BASE BASE
In implementation of the equation above, the factor transformations on
the right hand side of the product frame's definition are applied in
right-to-left order.
The ``from'' and ``to'' frames of a product frame definition may be completely arbitrary. The only restriction on these frames is that the transformation from each ``from'' frame to its corresponding ``to'' frame must be computable by Icy at the time the product frame is used. Note that because product frames are parameterized dynamic frames, limits on recursion depth for dynamic frames imply that while the factors may be dynamic frames, they may not be dynamic frames that require a level of recursion in order to evaluate their orientation. Defining a Product Frame in a Frame KernelSpecifying the Base Frame
FRAME_<frame_ID>_RELATIVE = '<frame_name>' Specifying the Frame Family
FRAME_<frame_ID>_FAMILY = 'PRODUCT' Specifying the Factors
FRAME_<frame_ID>_FROM_FRAMES = ( <from_frame 1> ... <from_frame N> ) FRAME_<frame_ID>_TO_FRAMES = ( <to_frame 1> ... <to_frame N> )The ``from'' and ``to'' frames must be specified by name. The Ith elements of the respective right-hand-side vectors of ``from'' and ``to'' frame names define the Ith factor transformation. The order of the factors in the kernel variables is the same as the order of the factors in the transformation product. When a vector is transformed from the base frame to the product frame, the transformations defined by the factors are applied in right-to-left order: the factor defined by the frames indexed by ``N'' is applied first. Dynamic Frame Implementation ConsiderationsIntroduction
Simulated RecursionThe Need for Recursion in the Icy Frame Subsystem
A -> BA procedure R_0 is ``recursive'' if it calls itself
R_0 -> R_0or if some sequence of calls initiated in the procedure R_0 results in a call to R_0:
R_0 -> R_1-> ... -> R_0ANSI standard Fortran 77 doesn't permit recursive calls. However, the implementation of two-vector frames requires sequences of calls that at face value are recursive. For example, to look up a state vector in the GSE frame (see the appendix ``Frame Definition Examples''), the procedure SPKEZ must initiate the sequence of calls (ellipses indicate omitted portions of the call graph)
SPKEZ -> ... -> FRMGET -> ... -> SPKEZ -> ... -> FRMGETBoth SPKEZ and FRMGET are called recursively in this graph. This issue affects not only SPICELIB but CSPICE and Icy as well because these products rely on the SPICELIB (Fortran) implementation of the frame subsystem. Implementation of Limited Simulated Recursion
SPKEZ -> ... -> FRMGET -> ... -> SPKEZ -> ... -> FRMGETis implemented in (valid) ANSI standard Fortran 77 using the call graph
SPKEZ -> ... -> FRMGET -> ... -> ZZSPKEZ0 -> ... -> ZZFRMGT0To a limited extent, two levels of simulated recursion are supported in the frame subsystem, so call graphs of the form
SPKEZ -> ... -> FRMGET -> ... -> ZZSPKEZ0 -> ... -> ZZFRMGT0
-> ... -> ZZSPKEZ1 -> ... -> ZZFRMGT1
are possible.
For brevity, when we refer to recursion in the following discussion, we'll omit the qualifier ``simulated.'' Limits on Recursion in Frame Definitions
cspice_spkezr, moon, et, 'GSE', 'NONE', 'EARTH', state, ltime cspice_sxform, 'GSE', 'J2000', et, xformboth cause the GSE parameterized dynamic frame to be evaluated at ET. When the definition of a parameterized dynamic frame F1 refers to a second frame F2 as
If F2 is not dynamic but its evaluation requires evaluation of a dynamic frame F3, the same restrictions apply to F3. When a dynamic frame is used as a base frame in either an SPK or CK segment, evaluation of data from that segment may result in a call to the dynamic frame subsystem. That call may result in lookup of another segment whose base frame is dynamic, and so on: the original kernel lookup could easily exhaust the dynamic frame subsystem's ability to handle recursive calls. Clearly use of dynamic frames in SPK and CK files requires caution. However, there are some ``reasonable'' applications that call for dynamic base frames in kernels, for example: representing ephemerides of earth orbiters expressed relative to the earth true equator and equinox of date frame. Frame Derivative Accuracy
Degenerate Geometry
Because two-vector frame definitions may be perfectly valid for some epochs and yield degenerate geometry for others, testing can easily fail to reveal problems with these definitions. Careful frame design is the best defense. As a backup measure, setting the angular separation tolerance in two-vector frame definitions can enable the frame subsystem to diagnose at run time degenerate or near-degenerate geometry. See the section ``Specifying the Angular Separation Tolerance'' above for details. Efficiency Concerns
To minimize the performance degradation imposed by recursion, avoid unnecessary references to dynamic frames in frame definitions. When possible, use J2000 or another inertial frame as the base frame, or as the frame relative to which constant or velocity vectors are defined. When it is not possible to use an inertial frame, prefer non-dynamic, non-inertial frames to dynamic frames. Switch Frames
Switch frames extend the flexibility of the SPICE frame subsystem by allowing a user-defined frame to rely on different data sources at different times. For example:
If base frames of a switch frame don't have associated time intervals, the base frames are applicable for all request times. A switch frame selects a base frame as follows: given a request time, the switch frame subsystem attempts to obtain orientation data from the highest priority, applicable base frame. If that base frame is a CK frame and data are unavailable, the next applicable frame in the base frame list is used, and so on. If an applicable base frame is not a CK frame and requested data are unavailable, an error is signaled. The orientation and optional angular velocity of the switch frame are those of the selected base frame. Specifying Switch Frames
FRAME_<name> = <ID code> FRAME_<ID code>_NAME = '<name>' FRAME_<ID code>_CLASS = 6 FRAME_<ID code>_CLASS_ID = <frame class ID> FRAME_<ID code>_CENTER = <center ID code or name> The Base Frame List
FRAME_<ID code>_ALIGNED_WITH = (
< lowest priority base frame ID or name >
< next-lowest priority base frame ID or name >
...
< highest priority base frame ID or name > )
All base frames of a given switch frame must be specified by name, or
all must be specified by frame ID code.
All base frames of a switch frame must have specifications available at the time the switch frame is used. This applies even to CK base frames. Note that CK frame ID codes and frame class ID codes are not required to match; the latter is the ID stored in CK files. It is the frame ID code that's required in the base frame list; this is provided by a CK frame specification. A base frame may occur multiple times in the base frame list. This can be useful for base frame lists that have associated time intervals. Time Intervals Associated with Base Frames
FRAME_<ID code>_START = (
< start time for lowest priority base frame >
< start time for next-lowest priority base frame >
...
< start time for highest priority base frame> )
FRAME_<ID code>_STOP = (
< stop time for lowest priority base frame >
< stop time for next-lowest priority base frame >
...
< stop time for highest priority base frame> )
If time intervals are provided for a switch frame, the count of start
times must match the count of stop times, and each must match the count
of entries in the base frame list.
Start and stop times may be specified by single-quoted time strings, double precision numbers, or as times using the text kernel ``@ format.'' For example:
'2021-12-31T12:00:00' 694224069.183907 6.94224069183907E+08 @2021-DEC-31/12:01:09.183907Times provided as single-quoted strings must be accepted by the Icy procedure cspice_str2et. A leapseconds kernel must be loaded in order to use such time strings. Numeric values are interpreted as seconds past J2000 TDB. Times in text kernel time format are interpreted as TDB calendar dates. Use of times in either of these formats does not require a leapseconds kernel. See the Kernel Required Reading kernel.req for details concerning the text kernel time format and accepted formats of double precision values. Each list of times for a given switch frame must be specified by values of the same type: string or numeric. Times in text kernel format are actually considered to be numeric values. The types used for a switch frame's list of start times and for its list of stop times need not match, but use of consistent types is recommended for readability. Binary Search
A switch frame is eligible for binary search if:
Switch Frame Connections
Switch Frame Buffering
It is possible for a user application to use many more switch frames than can be buffered concurrently, but changing the buffer contents with high frequency is inefficient. The buffer limits shown below are hard-coded. They may be increased in future versions of Icy.
Appendix. ``Built in'' Inertial Reference FramesComplete List of ``Built in'' Inertial Reference Frames
ID Name Description
----- -------- -------------------------------------------
1 J2000 Earth mean equator, dynamical equinox of J2000.
The root reference frame for SPICE.
2 B1950 Earth mean equator, dynamical equinox of B1950.
The B1950 reference frame is obtained by
precessing the J2000 frame backwards from
Julian year 2000 to Besselian year 1950, using
the 1976 IAU precession model.
The rotation from B1950 to J2000 is
[ -z ] [ theta ] [ -zeta ]
3 2 3
The values for z, theta, and zeta are computed
from the formulas given in table 5 of [5].
z = 1153.04066200330"
theta = 1002.26108439117"
zeta = 1152.84248596724"
3 FK4 Fundamental Catalog (4). The FK4 reference
frame is derived from the B1950 frame by
applying the equinox offset determined by
Fricke.
[ 0.525" ]
3
4 DE-118 JPL Developmental Ephemeris (118). The DE-118
reference frame is nearly identical to the FK4
frame. It is also derived from the B1950 frame.
Only the offset is different
[ 0.53155" ]
3
In [2], Standish uses two separate rotations,
[ 0.00073" ] P [ 0.5316" ]
3 3
(where P is the precession matrix used above to
define the B1950 frame). The major effect of the
second rotation is to correct for truncating the
magnitude of the first rotation. At his
suggestion, we will use the untruncated value,
and stick to a single rotation.
Most of the other DE historical reference frames
are defined relative to either the DE-118 or
B1950 frame. The values below are taken
from [4].
DE number Offset from DE-118 Offset from B1950
--------- ------------------ -----------------
96 +0.1209" +0.4107"
102 +0.3956" +0.1359"
108 +0.0541" +0.4775"
111 -0.0564" +0.5880"
114 -0.0213" +0.5529"
122 +0.0000" +0.5316"
125 -0.0438" +0.5754"
130 +0.0069" +0.5247"
5 DE-96 JPL Developmental Ephemeris ( 96).
6 DE-102 JPL Developmental Ephemeris (102).
7 DE-108 JPL Developmental Ephemeris (108).
8 DE-111 JPL Developmental Ephemeris (111).
9 DE-114 JPL Developmental Ephemeris (114).
10 DE-122 JPL Developmental Ephemeris (122).
11 DE-125 JPL Developmental Ephemeris (125).
12 DE-130 JPL Developmental Ephemeris (130).
13 GALACTIC Galactic System II. The Galactic System II
reference frame is defined by the following
rotations:
o o o
[ 327 ] [ 62.6 ] [ 282.25 ]
3 1 3
In the absence of better information, we
assume the rotations are relative to the
FK4 frame.
14 DE-200 JPL Developmental Ephemeris (200).
15 DE-202 JPL Developmental Ephemeris (202).
16 MARSIAU Mars Mean Equator and IAU vector of
J2000. The IAU-vector at Mars is the point
on the mean equator of Mars where the equator
ascends through the earth mean equator.
This vector is the cross product of Earth
mean north with Mars mean north.
17 ECLIPJ2000 Ecliptic coordinates based upon the
J2000 frame.
The value for the obliquity of the
ecliptic at J2000 is taken from page 114
of [7] equation 3.222-1. This agrees with the
expression given in [5].
18 ECLIPB1950 Ecliptic coordinates based upon the B1950
frame.
The value for the obliquity of the ecliptic at
B1950 is taken from page 171 of [7].
19 DE-140 JPL Developmental Ephemeris. (140)
The DE-140 frame is the DE-400 frame rotated:
0.9999256765384668 0.0111817701197967 0.0048589521583895
-0.0111817701797229 0.9999374816848701 -0.0000271545195858
-0.0048589520204830 -0.0000271791849815 0.9999881948535965
The DE-400 frame is treated as equivalent to
the J2000 frame.
20 DE-142 JPL Developmental Ephemeris. (142)
The DE-142 frame is the DE-402 frame rotated:
0.9999256765402605 0.0111817697320531 0.0048589526815484
-0.0111817697907755 0.9999374816892126 -0.0000271547693170
-0.0048589525464121 -0.0000271789392288 0.9999881948510477
The DE-402 frame is treated as equivalent to
the J2000 frame.
21 DE-143 JPL Developmental Ephemeris. (143)
The DE-143 frame is the DE-403 frame rotated:
0.9999256765435852 0.0111817743077255 0.0048589414674762
-0.0111817743300355 0.9999374816382505 -0.0000271622115251
-0.0048589414161348 -0.0000271713942366 0.9999881949053349
The DE-403 frame is treated as equivalent to
the J2000 frame.
Inertial Reference Frame References
[1] Jay Lieske, ``Precession Matrix Based on IAU (1976)
System of Astronomical Constants,'' Astron. Astrophys.
73, 282-284 (1979).
[2] E.M. Standish, Jr., ``Orientation of the JPL Ephemerides,
DE 200/LE 200, to the Dynamical Equinox of J2000,''
Astron. Astrophys. 114, 297-302 (1982).
[3] E.M. Standish, Jr., ``Conversion of Ephemeris Coordinates
from the B1950 System to the J2000 System,'' JPL IOM
314.6-581, 24 June 1985.
[4] E.M. Standish, Jr., ``The Equinox Offsets of the JPL
Ephemeris,'' JPL IOM 314.6-929, 26 February 1988.
[5] Jay Lieske, ``Expressions for the Precession Quantities
Based upon the IAU (1976) System of Astronomical
Constants'' Astron. Astrophys. 58, 1-16 (1977).
[6] Laura Bass and Robert Cesarone "Mars Observer Planetary
Constants and Models" JPL D-3444 November 1990.
[7] "Explanatory Supplement to the Astronomical Almanac"
edited by P. Kenneth Seidelmann. University Science
Books, 20 Edgehill Road, Mill Valley, CA 94941 (1992)
Low Level Inertial Reference Frame Procedures
Appendix. ``Built in'' PCK-Based IAU Body-Fixed Reference Frames
IAU_52_EUROPA IAU_ADRASTEA IAU_AMALTHEA IAU_ANANKE IAU_ARIEL IAU_ARROKOTH IAU_ATLAS IAU_BELINDA IAU_BENNU IAU_BIANCA IAU_BORRELLY IAU_CALLIRRHOE IAU_CALLISTO IAU_CALYPSO IAU_CARME IAU_CERES IAU_CHALDENE IAU_CHARON IAU_CORDELIA IAU_CRESSIDA IAU_DAVIDA IAU_DEIMOS IAU_DESDEMONA IAU_DESPINA IAU_DIDYMOS IAU_DIMORPHOS IAU_DIONE IAU_DONALDJOHANSON IAU_EARTH IAU_ELARA IAU_ENCELADUS IAU_EPIMETHEUS IAU_ERINOME IAU_EROS IAU_EUROPA IAU_EURYBATES IAU_GALATEA IAU_GANYMEDE IAU_GASPRA IAU_HARPALYKE IAU_HELENE IAU_HIMALIA IAU_HYDRA IAU_HYPERION IAU_IAPETUS IAU_IDA IAU_IO IAU_IOCASTE IAU_ISONOE IAU_ITOKAWA IAU_JANUS IAU_JULIET IAU_JUPITER IAU_KALYKE IAU_LARISSA IAU_LEDA IAU_LEUCUS IAU_LUTETIA IAU_LYSITHEA IAU_MAGACLITE IAU_MARS IAU_MENOETIUS IAU_MERCURY IAU_METIS IAU_MIMAS IAU_MIRANDA IAU_MOON IAU_NAIAD IAU_NEPTUNE IAU_NEREID IAU_NIX IAU_OBERON IAU_OPHELIA IAU_ORUS IAU_PALLAS IAU_PAN IAU_PANDORA IAU_PASIPHAE IAU_PATROCLUS IAU_PHOBOS IAU_PHOEBE IAU_PLUTO IAU_POLYMELE IAU_PORTIA IAU_PRAXIDIKE IAU_PROMETHEUS IAU_PROTEUS IAU_PUCK IAU_QUETA IAU_RHEA IAU_ROSALIND IAU_RYUGU IAU_SATURN IAU_SINOPE IAU_STEINS IAU_SUN IAU_TAYGETE IAU_TELESTO IAU_TEMPEL_1 IAU_TETHYS IAU_THALASSA IAU_THEBE IAU_THEMISTO IAU_TITAN IAU_TITANIA IAU_TRITON IAU_UMBRIEL IAU_URANUS IAU_VENUS IAU_VESTA Appendix. High Precision Earth Fixed Frames
ITRF93 EARTH_FIXED'ITRF93' is a frame ``fixed'' to the Earth's crust. It provides a high precision model for the orientation of the Earth with respect to J2000. In SPICE this is also a PCK type frame but its orientation is provided in a binary PCK file. 'EARTH_FIXED' is a ``generic frame'' that gives the orientation of the Earth with respect to some other frame (usually 'IAU_EARTH' or 'ITRF93') via a constant rotational offset. Such frames are called Text Kernel (TK) frames. See the subsection `` Gaining Flexibility via TK Frames'' for a discussion of the use of TK frames. Appendix. Frame Identifiers Reserved for Earth Fixed Frames
The class ID to associate with any DSN frame is the frame ID minus 10000. For example, the class ID associated with frame 13003 is 3003. It is this class ID that should be placed in the PCK file that implements the relationship between the DSN frame and the corresponding inertial frame. The center of any DSN frame is the center of mass of the Earth, which has SPK ID code 399. These frames are partially ``built in''. Given a frame ID in the range from 13001 to 13999, the frame subsystem ``knows'' that the frame is a PCK frame, the center of the frame is 399 and the class ID of the frame is the frame ID - 10000. This knowledge cannot be overridden. However, the frame subsystem does not ``know'' the relationship between the names of these frames and their ID codes. The relationship must be specified via the appropriate kernel pool frame definition.
FRAME_<name> = <DSN Frame-ID>
FRAME_<DSN Frame-ID>_NAME = '<name>'
OBJECT_EARTH_FRAME = <DSN Frame-ID>
Note that this specification leaves out the items below
FRAME_<DSN Frame-ID>_CENTER = 399 FRAME_<DSN Frame-ID>_CLASS = 2 FRAME_<DSN Frame-ID>_CLASS_ID = <DSN Frame-ID - 10000>You may supply these values if you like, but they have no effect on the frame subsystem's recognition and interpretation of the frame with the specified frame ID. Appendix. Frame Definition Examples
Inertial Frames
Aliases for inertial frames can be defined; see the section below on creating aliases using TK frames. PCK Frames
\begindata
FRAME_EROS_FIXED = 2000433
FRAME_2000433_NAME = 'EROS_FIXED'
FRAME_2000433_CLASS = 2
FRAME_2000433_CLASS_ID = 2000433
FRAME_2000433_CENTER = 2000433
OBJECT_2000433_FRAME = 'EROS_FIXED'
\begintext
CK Frames
\begindata
FRAME_MGS_SPACECRAFT = -94000
FRAME_-94000_NAME = 'MGS_SPACECRAFT'
FRAME_-94000_CLASS = 3
FRAME_-94000_CLASS_ID = -94000
FRAME_-94000_CENTER = -94
CK_-94000_SCLK = -94
CK_-94000_SPK = -94
OBJECT_-94_FRAME = 'MGS_SPACECRAFT'
\begintext
TK frames
TK frame --- Alias
\begindata
FRAME_MARS_FIXED = 1400499
FRAME_1400499_NAME = 'MARS_FIXED'
FRAME_1400499_CLASS = 4
FRAME_1400499_CLASS_ID = 1400499
FRAME_1400499_CENTER = 499
OBJECT_499_FRAME = 'MARS_FIXED'
\begintext
To make this point to another frame just replace
'IAU_MARS' below with the name of that frame.
\begindata
TKFRAME_1400499_RELATIVE = 'IAU_MARS'
TKFRAME_1400499_SPEC = 'MATRIX'
TKFRAME_1400499_MATRIX = ( 1 0 0
0 1 0
0 0 1 )
\begintext
TK frame --- Topographic
\begindata
FRAME_DSS-17_TOPO = 1399017
FRAME_1399017_NAME = 'DSS-17_TOPO'
FRAME_1399017_CLASS = 4
FRAME_1399017_CLASS_ID = 1399017
FRAME_1399017_CENTER = 399017
OBJECT_399017_FRAME = 'DSS-17_TOPO'
\begintext
Note that the geodetic longitude and co-latitude of the DSS-17
tracking station are: 243.126496675 and 54.657822839 respectively.
\begindata
TKFRAME_DSS-17_TOPO_RELATIVE = 'EARTH_FIXED'
TKFRAME_DSS-17_TOPO_SPEC = 'ANGLES'
TKFRAME_DSS-17_TOPO_UNITS = 'DEGREES'
TKFRAME_DSS-17_TOPO_AXES = ( 3, 2, 3 )
TKFRAME_DSS-17_TOPO_ANGLES = ( -243.126496675,
-54.657822839,
180.0 )
\begintext
Recall that the frame `EARTH_FIXED' is a TK frame. As a result
its relationship to other frames must be specified via
a kernel pool variable. We make that specification here.
If the ITRF93 PCK kernel is not available we can simply rename the
"RELATIVE" frame to be IAU_EARTH and still have the topocentric
frame well defined.
\begindata
TKFRAME_EARTH_FIXED_RELATIVE = 'ITRF93'
TKFRAME_EARTH_FIXED_SPEC = 'MATRIX'
TKFRAME_EARTH_FIXED_MATRIX = ( 1 0 0
0 1 0
0 0 1 )
\begintext
TK frame --- Instrument
The rotation from the DIF spacecraft frame to the MRI instrument frame determined from the in-flight calibration data can be represented by the following rotation angles:
mri
M = |0.129539306414| * |-45.006884881185| * |0.004898709285|
sc Z Y X
The frame definition contains the opposite of these rotation angles --
with the angle order reversed and the angle signs changed to the
opposite ones -- because the angles specified in it define the
transformation from the MRI frame to the spacecraft frame.
\begindata
FRAME_DIF_MRI = -140200
FRAME_-140200_NAME = 'DIF_MRI'
FRAME_-140200_CLASS = 4
FRAME_-140200_CLASS_ID = -140200
FRAME_-140200_CENTER = -140
TKFRAME_-140200_SPEC = 'ANGLES'
TKFRAME_-140200_RELATIVE = 'DIF_SPACECRAFT'
TKFRAME_-140200_ANGLES = ( -0.004898709285,
45.006884881185,
-0.129539306414 )
TKFRAME_-140200_AXES = ( 1, 2, 3 )
TKFRAME_-140200_UNITS = 'DEGREES'
\begintext
Examples of Two-Vector Parameterized Dynamic FramesGeocentric Solar Ecliptic (GSE) Frame
FRAME_GSE = <frame_ID> FRAME_<frame_ID>_NAME = 'GSE' FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'X' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_PRI_OBSERVER = 'EARTH' FRAME_<frame_ID>_PRI_TARGET = 'SUN' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = 'Y' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY' FRAME_<frame_ID>_SEC_OBSERVER = 'EARTH' FRAME_<frame_ID>_SEC_TARGET = 'SUN' FRAME_<frame_ID>_SEC_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_FRAME = 'J2000' Geocentric Solar Magnetospheric (GSM) Frame
FRAME_GSM = <frame_ID> FRAME_<frame_ID>_NAME = 'GSM' FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'X' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_PRI_OBSERVER = 'EARTH' FRAME_<frame_ID>_PRI_TARGET = 'SUN' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = 'Z' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_SEC_FRAME = 'IAU_EARTH' FRAME_<frame_ID>_SEC_SPEC = 'LATITUDINAL' FRAME_<frame_ID>_SEC_UNITS = 'DEGREES' FRAME_<frame_ID>_SEC_LONGITUDE = 288.43 FRAME_<frame_ID>_SEC_LATITUDE = 79.54 Mercury Solar Equatorial (MSEQ) Frame
The MSEQ frame can be defined using the following assignments, where <frame_ID> must be replaced by an integer ID code.
FRAME_MSEQ = <frame_ID> FRAME_<frame_ID>_NAME = 'MSEQ' FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 199 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'Z' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_PRI_FRAME = 'IAU_SUN' FRAME_<frame_ID>_PRI_SPEC = 'RECTANGULAR' FRAME_<frame_ID>_PRI_VECTOR = ( 0, 0, 1 ) FRAME_<frame_ID>_SEC_AXIS = 'X' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_SEC_OBSERVER = 'MERCURY' FRAME_<frame_ID>_SEC_TARGET = 'SUN' FRAME_<frame_ID>_SEC_ABCORR = 'NONE' Example: Nadir Frame for Mars Orbiting Spacecraft
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = <orbiter_ID> FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'Z' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'TARGET_NEAR_POINT' FRAME_<frame_ID>_PRI_OBSERVER = <orbiter_ID/name> FRAME_<frame_ID>_PRI_TARGET = 'MARS' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = '-X' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'OBSERVER_TARGET_VELOCITY' FRAME_<frame_ID>_SEC_OBSERVER = <orbiter_ID/name> FRAME_<frame_ID>_SEC_TARGET = 'MARS' FRAME_<frame_ID>_SEC_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_FRAME = 'J2000' Example: Roll-Celestial Spacecraft Frame
Definition of the roll-celestial frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = <spacecraft_ID> FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TWO-VECTOR' FRAME_<frame_ID>_PRI_AXIS = 'Z' FRAME_<frame_ID>_PRI_VECTOR_DEF = 'OBSERVER_TARGET_POSITION' FRAME_<frame_ID>_PRI_OBSERVER = <spacecraft_ID/name> FRAME_<frame_ID>_PRI_TARGET = 'EARTH' FRAME_<frame_ID>_PRI_ABCORR = 'NONE' FRAME_<frame_ID>_SEC_AXIS = 'X' FRAME_<frame_ID>_SEC_VECTOR_DEF = 'CONSTANT' FRAME_<frame_ID>_SEC_FRAME = 'J2000' FRAME_<frame_ID>_SEC_SPEC = 'RA/DEC' FRAME_<frame_ID>_SEC_UNITS = 'DEGREES' FRAME_<frame_ID>_SEC_RA = <star RA in degrees> FRAME_<frame_ID>_SEC_DEC = <star DEC in degrees> FRAME_<frame_ID>_SEC_ABCORR = 'S' FRAME_<frame_ID>_SEC_OBSERVER = <spacecraft_ID/name> Examples of Mean Equator and Equinox of Date FramesEarth Mean Equator and Equinox of Date Frames
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_ROTATION_STATE= 'ROTATING'Definition for the inertial version of the above frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_ROTATION_STATE= 'INERTIAL'Definition for the frozen version of the above frame, where the ``freeze epoch'' is B1950 TDB. The resulting frame should match the inertial frame B1950 to round-off level:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901 Examples of True Equator and Equinox of Date Frames
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'ROTATING'Definition for the inertial version of the above frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'INERTIAL'Definition for the frozen version of the above frame, where the ``freeze epoch'' is B1950 TDB.
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_NUT_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901 Example of a Mean Ecliptic and Equinox of Date Frame
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'ROTATING'Definition for the inertial version of the above frame:
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_ROTATION_STATE= 'INERTIAL'Definition for the frozen version of the above frame, where the ``freeze epoch'' is B1950 TDB.
FRAME_<frame_name> = <frame_ID> FRAME_<frame_ID>_NAME = <frame_name> FRAME_<frame_ID>_CLASS = 5 FRAME_<frame_ID>_CLASS_ID = <frame_ID> FRAME_<frame_ID>_CENTER = 399 FRAME_<frame_ID>_RELATIVE = 'J2000' FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED' FRAME_<frame_ID>_FAMILY = 'MEAN_ECLIPTIC_AND_EQUINOX_OF_DATE' FRAME_<frame_ID>_PREC_MODEL = 'EARTH_IAU_1976' FRAME_<frame_ID>_OBLIQ_MODEL = 'EARTH_IAU_1980' FRAME_<frame_ID>_FREEZE_EPOCH = @1949-DEC-31/22:09:46.861901 Example of an Euler Frame
The PCK data defining the underlying IAU_MARS frame are:
BODY499_POLE_RA = ( 317.68143 -0.1061 0. ) BODY499_POLE_DEC = ( 52.88650 -0.0609 0. ) BODY499_PM = ( 176.630 350.89198226 0. )These values are from:
Seidelmann, P.K., Abalakin, V.K., Bursa, M., Davies, M.E., Bergh, C. de, Lieske, J.H., Oberst, J., Simon, J.L., Standish, E.M., Stooke, P., and Thomas, P.C. (2002). "Report of the IAU/IAG Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites: 2000," Celestial Mechanics and Dynamical Astronomy, v.82, Issue 1, pp. 83-111.Here pole RA/Dec terms in the PCK are in degrees and degrees/century; the rates here have been converted to degrees/sec. Prime meridian terms in the PCK are in degrees and degrees/day; the rate here has been converted to degrees/sec. The 3x3 transformation matrix M defined by the angles is
M = [angle_1] [angle_2] [angle_3]
3 1 3
Vectors are mapped from the J2000 base frame to the IAU_MARS frame via
left multiplication by M.
The relationship of these Euler angles to RA/Dec/PM for the J2000-to-IAU Mars body-fixed transformation is as follows:
angle_1 is PM * (radians/degree) angle_2 is pi/2 - Dec * (radians/degree) angle_3 is pi/2 + RA * (radians/degree)Since when we define the IAU_MARS_EULER frame we're defining the *inverse* of the above transformation, the angles for our Euler frame definition are reversed and the signs negated:
angle_1 is -pi/2 - RA * (radians/degree) angle_2 is -pi/2 + Dec * (radians/degree) angle_3 is - PM * (radians/degree)Then our frame definition is:
FRAME_IAU_MARS_EULER = <frame_ID>
FRAME_<frame_ID>_NAME = 'IAU_MARS_EULER'
FRAME_<frame_ID>_CLASS = 5
FRAME_<frame_ID>_CLASS_ID = <frame_ID>
FRAME_<frame_ID>_CENTER = 499
FRAME_<frame_ID>_RELATIVE = 'J2000'
FRAME_<frame_ID>_DEF_STYLE = 'PARAMETERIZED'
FRAME_<frame_ID>_FAMILY = 'EULER'
FRAME_<frame_ID>_EPOCH = @2000-JAN-1/12:00:00
FRAME_<frame_ID>_AXES = ( 3 1 3 )
FRAME_<frame_ID>_UNITS = 'DEGREES'
FRAME_<frame_ID>_ANGLE_1_COEFFS = ( -47.68143
0.33621061170684714E-10 )
FRAME_<frame_ID>_ANGLE_2_COEFFS = ( -37.1135
-0.19298045478743630E-10 )
FRAME_<frame_ID>_ANGLE_3_COEFFS = ( -176.630
-0.40612497946759260E-02 )
Examples of Product FramesIAU_EARTH Frame, Augmented with Nutation Model
The EARTH_ROTATING frame defined uses the Earth spin angle relative to the mean equinox of date from the IAU_EARTH frame and pole and equinox from the Earth true equator and true equinox of date frame. While the pole direction of the IAU_EARTH frame reflects precession, the pole direction of this frame reflects both precession and nutation. The transformation from the J2000 frame to the product frame is defined by:
EARTH_ROTATING IAU_EARTH TETE
T = T * T
J2000 EME J2000
where the notation
B
T
A
indicates the transformation from frame A to frame B.
The specifications of the frame and of the two supporting frames EME and TETE are shown below.
\begindata FRAME_EARTH_ROTATING = 1890000 FRAME_1890000_NAME = 'EARTH_ROTATING' FRAME_1890000_CLASS = 5 FRAME_1890000_CLASS_ID = 1890000 FRAME_1890000_CENTER = 399 FRAME_1890000_RELATIVE = 'J2000' FRAME_1890000_DEF_STYLE = 'PARAMETERIZED' FRAME_1890000_FAMILY = 'PRODUCT' FRAME_1890000_ROTATION_STATE = 'ROTATING' FRAME_1890000_FROM_FRAMES = ( 'EME', 'J2000' ) FRAME_1890000_TO_FRAMES = ( 'IAU_EARTH', 'TETE' ) \begintext Earth mean equator and mean equinox of date frame "EME": \begindata FRAME_EME = 1890001 FRAME_1890001_NAME = 'EME' FRAME_1890001_CLASS = 5 FRAME_1890001_CLASS_ID = 1890001 FRAME_1890001_CENTER = 399 FRAME_1890001_RELATIVE = 'J2000' FRAME_1890001_DEF_STYLE = 'PARAMETERIZED' FRAME_1890001_FAMILY = 'MEAN_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_1890001_PREC_MODEL = 'EARTH_IAU_1976' FRAME_1890001_ROTATION_STATE = 'ROTATING' \begintext Earth true equator and true equinox of date frame "TETE": \begindata FRAME_TETE = 1890002 FRAME_1890002_NAME = 'TETE' FRAME_1890002_CLASS = 5 FRAME_1890002_CLASS_ID = 1890002 FRAME_1890002_CENTER = 399 FRAME_1890002_RELATIVE = 'J2000' FRAME_1890002_DEF_STYLE = 'PARAMETERIZED' FRAME_1890002_FAMILY = 'TRUE_EQUATOR_AND_EQUINOX_OF_DATE' FRAME_1890002_PREC_MODEL = 'EARTH_IAU_1976' FRAME_1890002_NUT_MODEL = 'EARTH_IAU_1980' FRAME_1890002_ROTATION_STATE = 'ROTATING' \begintextIn order for this frame to be generally useful, a more accurate Earth spin model than that provided by the IAU_EARTH frame would need to be used. In practice, high-precision binary Earth PCKs are more suitable as a source of accurate Earth orientation data. Dog-Leg Frame for Saturn
Examples of Switch Frames
Switch Frame Using Reconstructed and Predict CKs
The specification for such a switch frame would have the form:
\begindata
FRAME_SWITCH1 = -123001
FRAME_-123001_NAME = 'SWITCH1'
FRAME_-123001_CLASS = 6
FRAME_-123001_CLASS_ID = -123001
FRAME_-123001_CENTER = -123
FRAME_-123001_ALIGNED_WITH = (
'CK_PREDICTED'
'CK_RECONSTRUCTED'
)
\begintext
The base frames, which are specified by the assignment of the kernel
variable FRAME_-123001_ALIGNED_WITH, are listed in order of increasing
priority: given a request time, the SWITCH1 frame first tries to get
orientation of the frame CK_RECONSTRUCTED; if not found, it tries to get
orientation of the frame CK_PREDICTED.
The CK frames referenced by this switch frame must be defined, and the corresponding CKs loaded, along with associated SCLK kernels and a leapseconds kernel, for the switch frame to be usable. Loading the CKs without loading an FK that defines the CK frames would not work. Examples of the CK frame definitions are shown below. Reconstructed attitude CK frame:
\begindata FRAME_CK_RECONSTRUCTED = -123501 FRAME_-123501_NAME = 'CK_RECONSTRUCTED' FRAME_-123501_CLASS = 3 FRAME_-123501_CLASS_ID = -123601 FRAME_-123501_CENTER = -123 CK_-123501_SCLK = -123 \begintextPredicted attitude CK frame:
\begindata FRAME_CK_PREDICTED = -123502 FRAME_-123502_NAME = 'CK_PREDICTED' FRAME_-123502_CLASS = 3 FRAME_-123502_CLASS_ID = -123602 FRAME_-123502_CENTER = -123 CK_-123502_SCLK = -123000 \begintextBase frames may also be specified by frame ID, so the ``aligned with'' assignment may be written as
\begindata
FRAME_-123001_ALIGNED_WITH = (
-123502
-123501
)
\begintext
Note that the frame ID of a CK frame might not match the frame's frame
class ID, which is the ID used in CKs providing data for that frame. In
this case, the IDs used in reconstructed and predicted CKs would be
-123601 and -123602 respectively. Using those IDs in the ``aligned
with'' assignment would not work.
Switch Frame Using CK and Dynamic Frames
This example is for a seven year long mission:
launch -- 2018-01-01 orbit insertion -- 2018-10-01 end of mission -- 2025-01-01The CK frames are applicable for the entire mission. The nominal cruise attitude is implemented by the dynamic frame DYN_CRUISE (definition not shown). This frame is applicable only for the cruise phase of the mission. The nominal orbital attitude is implemented by the dynamic frame DYN_ORBIT (definition not shown). This frame is applicable only for the orbital phase of the mission. The CK frames are listed last in the set of base frame names, so they have highest priority. Start and stop times below are expressed in text kernel format. The times are interpreted as TDB calendar dates.
\begindata
FRAME_SWITCH2 = -123002
FRAME_-123002_NAME = 'SWITCH2'
FRAME_-123002_CLASS = 6
FRAME_-123002_CLASS_ID = -123001
FRAME_-123002_CENTER = -123
FRAME_-123002_ALIGNED_WITH = (
'DYN_CRUISE'
'DYN_ORBIT'
'CK_PREDICTED'
'CK_RECONSTRUCTED'
)
FRAME_-123002_START = (
@2018-01-01
@2018-10-01
@2018-01-01
@2018-01-01
)
FRAME_-123002_STOP = (
@2018-10-01
@2025-01-01
@2025-01-01
@2025-01-01
)
\begintext
Time strings recognized by the Icy procedure cspice_str2et also may be
used. We could define the interval start times using the assignment
\begindata
FRAME_-123002_START = (
'2018 JAN 1 00:00:00.000 TDB'
'2018 OCT 1 00:00:00.000 TDB'
'2018 JAN 1 00:00:00.000 TDB'
'2018 JAN 1 00:00:00.000 TDB'
)
\begintext
Predicted Attitude Profile for Observation Planning
This example is for two six-hour long orbits, each broken into equal chunks for Sun-pointing, Earth-pointing, and observation modes. Pointing transitions are abrupt: at each transition time, the switch frame instantaneously changes its orientation from that of one base frame that of the next. The nominal Sun-pointing attitude is implemented by the dynamic frame DYN_SUN_POINTING (definition not shown). The nominal Earth-pointing attitude is implemented by the dynamic frame DYN_EARTH_POINTING (definition not shown). The nominal observation attitude is implemented by the dynamic frame DYN_OBSERVATION (definition not shown).
\begindata
FRAME_SWITCH3 = -123003
FRAME_-123003_NAME = 'SWITCH3'
FRAME_-123003_CLASS = 6
FRAME_-123003_CLASS_ID = -123003
FRAME_-123003_CENTER = -123
FRAME_-123003_ALIGNED_WITH = (
'DYN_SUN_POINTING'
'DYN_EARTH_POINTING'
'DYN_OBSERVATION'
'DYN_SUN_POINTING'
'DYN_EARTH_POINTING'
'DYN_OBSERVATION'
)
FRAME_-123003_START = (
@2018-01-01/00:00:00
@2018-01-01/02:00:00
@2018-01-01/04:00:00
@2018-01-01/06:00:00
@2018-01-01/08:00:00
@2018-01-01/10:00:00
)
FRAME_-123003_STOP = (
@2018-01-01/02:00:00
@2018-01-01/04:00:00
@2018-01-01/06:00:00
@2018-01-01/08:00:00
@2018-01-01/10:00:00
@2018-01-01/12:00:00
)
\begintext
Because the time intervals associated with the base frames are listed in
increasing time order and overlap only at their endpoints, request times
will be mapped to time intervals by binary search. If the time intervals
were listed in any other order, a linear search would be used.
|