ckw02_c |

## Procedurevoid ckw02_c ( SpiceInt handle, SpiceDouble begtim, SpiceDouble endtim, SpiceInt inst, ConstSpiceChar * ref, ConstSpiceChar * segid, SpiceInt nrec, ConstSpiceDouble start [], ConstSpiceDouble stop [], ConstSpiceDouble quats [][4], ConstSpiceDouble avvs [][3], ConstSpiceDouble rates [] ) ## AbstractWrite a type 2 segment to a C-kernel. ## Required_ReadingCK DAF SCLK ## KeywordsPOINTING UTILITY ## Brief_I/OVariable I/O Description -------- --- -------------------------------------------------- handle I Handle of an open CK file. begtim I The beginning encoded SCLK of the segment. endtim I The ending encoded SCLK of the segment. inst I The NAIF instrument ID code. ref I The reference frame of the segment. segid I Segment identifier. nrec I Number of pointing records. start I Encoded SCLK interval start times. stop I Encoded SCLK interval stop times. quats I Quaternions representing instrument pointing. avvs I Angular velocity vectors. rates I Number of seconds per tick for each interval. ## Detailed_Inputhandle is the handle of the CK file to which the segment will be written. The file must have been opened with write access. begtim is the beginning encoded SCLK time of the segment. This value should be less than or equal to the first START time in the segment. endtim is the encoded SCLK time at which the segment ends. This value should be greater than or equal to the last STOP time in the segment. inst is the NAIF integer ID code for the instrument. ref is a character string that specifies the reference frame of the segment. This should be one of the frames supported by the SPICELIB routine NAMFRM which is an entry point of FRAMEX. segid is the segment identifier. A CK segment identifier may contain up to 40 characters. nrec is the number of pointing intervals that will be written to the segment. start are the start times of each interval in encoded spacecraft clock. These times must be strictly increasing. stop are the stop times of each interval in encoded spacecraft clock. These times must be greater than the START times that they correspond to but less than or equal to the START time of the next interval. quats are the quaternions representing the C-matrices associated with the start times of each interval. See the discussion of "Quaternion Styles" in the Particulars section below. AVVS are the angular velocity vectors for each interval. RATES are the number of seconds per encoded spacecraft clock tick for each interval. In most applications this value will be the same for each interval within a segment. For example, when constructing a predict C-kernel for Mars Observer, the rate would be 1/256 for each interval since this is the smallest time unit expressible by the MO clock. The nominal seconds per tick rates for Galileo and Voyager are 1/120 and 0.06 respectively. ## Detailed_OutputNone. See Files section. ## ParametersNone. ## Exceptions1) If handle is not the handle of a C-kernel opened for writing the error will be diagnosed by routines called by this routine. 2) If segid is more than 40 characters long, the error SPICE(SEGIDTOOLONG) is signaled. 3) If segid contains any nonprintable characters, the error SPICE(NONPRINTABLECHARS) is signaled. 4) If the first START time is negative, the error SPICE(INVALIDSCLKTIME) is signaled. If any of the subsequent START times are negative the error SPICE(TIMESOUTOFORDER) will be signaled. 5) If any of the STOP times are negative, the error SPICE(DEGENERATEINTERVAL) is signaled. 6) If the STOP time of any of the intervals is less than or equal to the START time, the error SPICE(DEGENERATEINTERVAL) is signaled. 7) If the START times are not strictly increasing, the error SPICE(TIMESOUTOFORDER) is signaled. 8) If the STOP time of one interval is greater than the START time of the next interval, the error SPICE(BADSTOPTIME) is signaled. 9) If begtim is greater than START[0] or endtim is less than STOP[NREC-1], the error SPICE(INVALIDDESCRTIME) is signaled. 10) If the name of the reference frame is not one of those supported by the routine NAMFRM, the error SPICE(INVALIDREFFRAME) is signaled. 11) If nrec, the number of pointing records, is less than or equal to 0, the error SPICE(INVALIDNUMRECS) is signaled. 12) If any quaternion has magnitude zero, the error SPICE(ZEROQUATERNION) is signaled. ## FilesThis routine adds a type 2 segment to a C-kernel. The C-kernel may be either a new one or an existing one opened for writing. ## ParticularsFor a detailed description of a type 2 CK segment please see the CK Required Reading. This routine relieves the user from performing the repetitive calls to the DAF routines necessary to construct a CK segment. Quaternion Styles ----------------- There are different "styles" of quaternions used in science and engineering applications. Quaternion styles are characterized by - The order of quaternion elements - The quaternion multiplication formula - The convention for associating quaternions with rotation matrices Two of the commonly used styles are - "SPICE" > Invented by Sir William Rowan Hamilton > Frequently used in mathematics and physics textbooks - "Engineering" > Widely used in aerospace engineering applications CSPICE function interfaces ALWAYS use SPICE quaternions. Quaternions of any other style must be converted to SPICE quaternions before they are passed to CSPICE functions. Relationship between SPICE and Engineering Quaternions ------------------------------------------------------ Let M be a rotation matrix such that for any vector V, M*V is the result of rotating V by theta radians in the counterclockwise direction about unit rotation axis vector A. Then the SPICE quaternions representing M are (+/-) ( cos(theta/2), sin(theta/2) A(1), sin(theta/2) A(2), sin(theta/2) A(3) ) while the engineering quaternions representing M are (+/-) ( -sin(theta/2) A(1), -sin(theta/2) A(2), -sin(theta/2) A(3), cos(theta/2) ) For both styles of quaternions, if a quaternion q represents a rotation matrix M, then -q represents M as well. Given an engineering quaternion QENG = ( q0, q1, q2, q3 ) the equivalent SPICE quaternion is QSPICE = ( q3, -q0, -q1, -q2 ) Associating SPICE Quaternions with Rotation Matrices ---------------------------------------------------- Let FROM and TO be two right-handed reference frames, for example, an inertial frame and a spacecraft-fixed frame. Let the symbols V , V FROM TO denote, respectively, an arbitrary vector expressed relative to the FROM and TO frames. Let M denote the transformation matrix that transforms vectors from frame FROM to frame TO; then V = M * V TO FROM where the expression on the right hand side represents left multiplication of the vector by the matrix. Then if the unit-length SPICE quaternion q represents M, where q = (q0, q1, q2, q3) the elements of M are derived from the elements of q as follows: +- -+ | 2 2 | | 1 - 2*( q2 + q3 ) 2*(q1*q2 - q0*q3) 2*(q1*q3 + q0*q2) | | | | | | 2 2 | M = | 2*(q1*q2 + q0*q3) 1 - 2*( q1 + q3 ) 2*(q2*q3 - q0*q1) | | | | | | 2 2 | | 2*(q1*q3 - q0*q2) 2*(q2*q3 + q0*q1) 1 - 2*( q1 + q2 ) | | | +- -+ Note that substituting the elements of -q for those of q in the right hand side leaves each element of M unchanged; this shows that if a quaternion q represents a matrix M, then so does the quaternion -q. To map the rotation matrix M to a unit quaternion, we start by decomposing the rotation matrix as a sum of symmetric and skew-symmetric parts: 2 M = [ I + (1-cos(theta)) OMEGA ] + [ sin(theta) OMEGA ] symmetric skew-symmetric OMEGA is a skew-symmetric matrix of the form +- -+ | 0 -n3 n2 | | | OMEGA = | n3 0 -n1 | | | | -n2 n1 0 | +- -+ The vector N of matrix entries (n1, n2, n3) is the rotation axis of M and theta is M's rotation angle. Note that N and theta are not unique. Let C = cos(theta/2) S = sin(theta/2) Then the unit quaternions Q corresponding to M are Q = +/- ( C, S*n1, S*n2, S*n3 ) The mappings between quaternions and the corresponding rotations are carried out by the CSPICE routines q2m_c {quaternion to matrix} m2q_c {matrix to quaternion} m2q_c always returns a quaternion with scalar part greater than or equal to zero. SPICE Quaternion Multiplication Formula --------------------------------------- Given a SPICE quaternion Q = ( q0, q1, q2, q3 ) corresponding to rotation axis A and angle theta as above, we can represent Q using "scalar + vector" notation as follows: s = q0 = cos(theta/2) v = ( q1, q2, q3 ) = sin(theta/2) * A Q = s + v Let Q1 and Q2 be SPICE quaternions with respective scalar and vector parts s1, s2 and v1, v2: Q1 = s1 + v1 Q2 = s2 + v2 We represent the dot product of v1 and v2 by <v1, v2> and the cross product of v1 and v2 by v1 x v2 Then the SPICE quaternion product is Q1*Q2 = s1*s2 - <v1,v2> + s1*v2 + s2*v1 + (v1 x v2) If Q1 and Q2 represent the rotation matrices M1 and M2 respectively, then the quaternion product Q1*Q2 represents the matrix product M1*M2 ## ExamplesThis example writes a predict type 2 C-kernel segment for the Mars Observer spacecraft bus to a previously opened CK file attached to handle. /. Assume arrays of quaternions, angular velocities, and interval start and stop times are produced elsewhere. ./ . . . /. The nominal number of seconds in a tick for MO is 1/256. ./ sectik = 1. / 256.; for ( i = 0; i < nrec; i++ ) { rate[i] = sectik; } /. The subroutine ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) K.R. Gehringer (JPL) J.M. Lynch (JPL) ## Version-CSPICE Version 2.0.0, 01-JUN-2010 (NJB) The check for non-unit quaternions has been replaced with a check for zero-length quaternions. (The implementation of the check is located in ckw02_.) -CSPICE Version 1.2.1, 27-FEB-2008 (NJB) Updated header; added information about SPICE quaternion conventions. -CSPICE Version 1.2.0, 28-AUG-2001 (NJB) Changed prototype: inputs start, stop, sclkdp, quats, and avvs are now const-qualified. Implemented interface macros for casting these inputs to const. -CSPICE Version 1.1.0, 08-FEB-1998 (NJB) References to C2F_CreateStr_Sig were removed; code was cleaned up accordingly. String checks are now done using the macro CHKFSTR. -CSPICE Version 1.0.0, 25-OCT-1997 (NJB) Based on SPICELIB Version 2.0.0, 28-DEC-1993 (WLT) ## Index_Entrieswrite ck type_2 pointing data segment |

Wed Apr 5 17:54:30 2017