dpgrdr_c |

Table of contents## Proceduredpgrdr_c ( Derivative of planetographic w.r.t. rectangular ) void dpgrdr_c ( ConstSpiceChar * body, SpiceDouble x, SpiceDouble y, SpiceDouble z, SpiceDouble re, SpiceDouble f, SpiceDouble jacobi[3][3] ) ## AbstractCompute the Jacobian matrix of the transformation from rectangular to planetographic coordinates. ## Required_ReadingNone. ## KeywordsCOORDINATES DERIVATIVES MATRIX ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- body I Body with which coordinate system is associated. x I X-coordinate of point. y I Y-coordinate of point. z I Z-coordinate of point. re I Equatorial radius of the reference spheroid. f I Flattening coefficient. jacobi O Matrix of partial derivatives. ## Detailed_Inputbody is the name of the body with which the planetographic coordinate system is associated. `body' is used by this routine to look up from the kernel pool the prime meridian rate coefficient giving the body's spin sense. See the -Files and -Particulars header sections below for details. x, y, z are the rectangular coordinates of the point at which the Jacobian of the map from rectangular to planetographic coordinates is desired. re is the equatorial radius of the reference spheroid. This spheroid is a volume of revolution: its horizontal cross sections are circular. The shape of the spheroid is defined by an equatorial radius `re' and a polar radius `rp'. f is the flattening coefficient = (re-rp) / re where `rp' is the polar radius of the spheroid. The units of `rp' match those of `re'. (More importantly rp = re*(1-f) ) ## Detailed_Outputjacobi is the matrix of partial derivatives of the conversion from rectangular to planetographic coordinates. It has the form .- -. | dlon/dx dlon/dy dlon/dz | | dlat/dx dlat/dy dlat/dz | | dalt/dx dalt/dy dalt/dz | `- -' evaluated at the input values of `x', `y', and `z'. ## ParametersNone. ## Exceptions1) If the body name `body' cannot be mapped to a NAIF ID code, and if `body' is not a string representation of an integer, the error SPICE(IDCODENOTFOUND) is signaled by a routine in the call tree of this routine. 2) If the kernel variable BODY<ID code>_PGR_POSITIVE_LON is present in the kernel pool but has a value other than one of 'EAST' 'WEST' the error SPICE(INVALIDOPTION) is signaled by a routine in the call tree of this routine. Case and blanks are ignored when these values are interpreted. 3) If polynomial coefficients for the prime meridian of `body' are not available in the kernel pool, and if the kernel variable BODY<ID code>_PGR_POSITIVE_LON is not present in the kernel pool, the error SPICE(MISSINGDATA) is signaled by a routine in the call tree of this routine. 4) If the equatorial radius is non-positive, the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call tree of this routine. 5) If the flattening coefficient is greater than or equal to one, the error SPICE(VALUEOUTOFRANGE) is signaled by a routine in the call tree of this routine. 6) If the input point is on the Z-axis (X = 0 and Y = 0), the Jacobian matrix is undefined, an error is signaled by a routine in the call tree of this routine. 7) If the `body' input string pointer is null, the error SPICE(NULLPOINTER) is signaled. 8) If the `body' input string has zero length, the error SPICE(EMPTYSTRING) is signaled. ## FilesThis routine expects a kernel variable giving body's prime meridian angle as a function of time to be available in the kernel pool. Normally this item is provided by loading a PCK file. The required kernel variable is named BODY<body ID>_PM where <body ID> represents a string containing the NAIF integer ID code for `body'. For example, if `body' is "JUPITER", then the name of the kernel variable containing the prime meridian angle coefficients is BODY599_PM See the PCK Required Reading for details concerning the prime meridian kernel variable. The optional kernel variable BODY<body ID>_PGR_POSITIVE_LON also is normally defined via loading a text kernel. When this variable is present in the kernel pool, the prime meridian coefficients for `body' are not required by this routine. See the -Particulars section below for details. ## ParticularsWhen performing vector calculations with velocities it is usually most convenient to work in rectangular coordinates. However, once the vector manipulations have been performed, it is often desirable to convert the rectangular representations into planetographic coordinates to gain insights about phenomena in this coordinate frame. To transform rectangular velocities to derivatives of coordinates in a planetographic system, one uses the Jacobian of the transformation between the two systems. Given a state in rectangular coordinates ( x, y, z, dx, dy, dz ) the velocity in planetographic coordinates is given by the matrix equation: t | t (dlon, dlat, dalt) = jacobi| * (dx, dy, dz) |(x,y,z) This routine computes the matrix | jacobi| |(x, y, z) The planetographic definition of latitude is identical to the planetodetic (also called "geodetic" in SPICE documentation) definition. In the planetographic coordinate system, latitude is defined using a reference spheroid. The spheroid is characterized by an equatorial radius and a polar radius. For a point P on the spheroid, latitude is defined as the angle between the X-Y plane and the outward surface normal at P. For a point P off the spheroid, latitude is defined as the latitude of the nearest point to P on the spheroid. Note if P is an interior point, for example, if P is at the center of the spheroid, there may not be a unique nearest point to P. In the planetographic coordinate system, longitude is defined using the spin sense of the body. Longitude is positive to the west if the spin is prograde and positive to the east if the spin is retrograde. The spin sense is given by the sign of the first degree term of the time-dependent polynomial for the body's prime meridian Euler angle "W": the spin is retrograde if this term is negative and prograde otherwise. For the sun, planets, most natural satellites, and selected asteroids, the polynomial expression for W may be found in a SPICE PCK kernel. The earth, moon, and sun are exceptions: planetographic longitude is measured positive east for these bodies. If you wish to override the default sense of positive longitude for a particular body, you can do so by defining the kernel variable BODY<body ID>_PGR_POSITIVE_LON where <body ID> represents the NAIF ID code of the body. This variable may be assigned either of the values 'WEST' 'EAST' For example, you can have this routine treat the longitude of the earth as increasing to the west using the kernel variable assignment BODY399_PGR_POSITIVE_LON = 'WEST' Normally such assignments are made by placing them in a text kernel and loading that kernel via furnsh_c. The definition of this kernel variable controls the behavior of the CSPICE planetographic routines pgrrec_c recpgr_c ## ExamplesThe numerical results shown for this example may differ across platforms. The results depend on the SPICE kernels used as input, the compiler and supporting libraries, and the machine specific arithmetic implementation. 1) Find the planetographic state of the earth as seen from Mars in the J2000 reference frame at January 1, 2005 TDB. Map this state back to rectangular coordinates as a check. Use the meta-kernel shown below to load the required SPICE kernels. KPL/MK File name: dpgrdr_ex1.tm This meta-kernel is intended to support operation of SPICE example programs. The kernels shown here should not be assumed to contain adequate or correct versions of data required by SPICE-based user applications. In order for an application to use this meta-kernel, the kernels referenced here must be present in the user's current working directory. The names and contents of the kernels referenced by this meta-kernel are as follows: File name Contents --------- -------- de421.bsp Planetary ephemeris pck00008.tpc Planet orientation and radii naif0009.tls Leapseconds \begindata KERNELS_TO_LOAD = ( 'de421.bsp', 'pck00008.tpc', 'naif0009.tls' ) \begintext End of meta-kernel Example code begins here. /. Program dpgrdr_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main() { /. Local variables ./ SpiceDouble alt; SpiceDouble drectn [3]; SpiceDouble et; SpiceDouble f; SpiceDouble jacobi [3][3]; SpiceDouble lat; SpiceDouble lon; SpiceDouble lt; SpiceDouble pgrvel [3]; SpiceDouble radii [3]; SpiceDouble re; SpiceDouble rectan [3]; SpiceDouble rp; SpiceDouble state [6]; SpiceInt n; /. Load SPK, PCK, and LSK kernels, use a meta kernel for convenience. ./ furnsh_c ( "dpgrdr_ex1.tm" ); /. Look up the radii for Mars. Although we omit it here, we could first call badkpv_c to make sure the variable BODY499_RADII has three elements and numeric data type. If the variable is not present in the kernel pool, bodvrd_c will signal an error. ./ bodvrd_c ( "MARS", "RADII", 3, &n, radii ); /. Compute flattening coefficient. ./ re = radii[0]; rp = radii[2]; f = ( re - rp ) / re; /. Look up the geometric state of earth as seen from Mars at January 1, 2005 TDB, relative to the J2000 reference frame. ./ str2et_c ( "January 1, 2005 TDB", &et); spkezr_c ( "Earth", et, "J2000", "LT+S", "Mars", state, < ); /. Convert position to planetographic coordinates. ./ recpgr_c ( "mars", state, re, f, &lon, &lat, &alt ); /. Convert velocity to planetographic coordinates. ./ ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.L. Taber (JPL) ## Version-CSPICE Version 1.0.1, 10-AUG-2021 (JDR) Edited the header comments to comply with NAIF standard. Modified code example to use meta-kernel to load kernels. Updated example code to split printf statement in three in order to comply with ANSI-C maximum string literal of length. -CSPICE Version 1.0.0, 26-DEC-2004 (NJB) (WLT) ## Index_EntriesJacobian of planetographic w.r.t. rectangular coordinates |

Fri Dec 31 18:41:04 2021