drdsph_c |

Table of contents## Proceduredrdsph_c ( Derivative of rectangular w.r.t. spherical ) void drdsph_c ( SpiceDouble r, SpiceDouble colat, SpiceDouble slon, SpiceDouble jacobi[3][3] ) ## AbstractCompute the Jacobian matrix of the transformation from spherical to rectangular coordinates. ## Required_ReadingNone. ## KeywordsCOORDINATES DERIVATIVES MATRIX ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- r I Distance of a point from the origin. colat I Angle of the point from the positive z-axis. slon I Angle of the point from the xy plane. jacobi O Matrix of partial derivatives. ## Detailed_Inputr isn the distance of a point from the origin. colat is the angle between the point and the positive z-axis, in radians. slon is the angle of the point from the xz plane in radians. The angle increases in the counterclockwise sense about the +z axis. ## Detailed_Outputjacobi is the matrix of partial derivatives of the conversion between spherical and rectangular coordinates, evaluated at the input coordinates. This matrix has the form .- -. | dx/dr dx/dcolat dx/dslon | | | | dy/dr dy/dcolat dy/dslon | | | | dz/dr dz/dcolat dz/dslon | `- -' evaluated at the input values of `r', `slon' and `colat'. Here `x', `y', and `z' are given by the familiar formulae x = r*cos(slon)*sin(colat) y = r*sin(slon)*sin(colat) z = r*cos(colat) ## ParametersNone. ## ExceptionsError free. ## FilesNone. ## ParticularsIt is often convenient to describe the motion of an object in the spherical coordinate system. However, when performing vector computations its hard to beat rectangular coordinates. To transform states given with respect to spherical coordinates to states with respect to rectangular coordinates, one uses the Jacobian of the transformation between the two systems. Given a state in spherical coordinates ( r, colat, slon, dr, dcolat, dslon ) the velocity in rectangular coordinates is given by the matrix equation: t | t (dx, dy, dz) = jacobi| * (dr, dcolat, dslon ) |(r,colat,slon) This routine computes the matrix | jacobi| |(r,colat,slon) ## 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 spherical state of the Earth as seen from Mars in the IAU_MARS 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: drdsph_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 pck00010.tpc Planet orientation and radii naif0009.tls Leapseconds \begindata KERNELS_TO_LOAD = ( 'de421.bsp', 'pck00010.tpc', 'naif0009.tls' ) \begintext End of meta-kernel Example code begins here. /. Program drdsph_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables ./ SpiceDouble colat; SpiceDouble drectn [3]; SpiceDouble et; SpiceDouble jacobi [3][3]; SpiceDouble lt; SpiceDouble sphvel [3]; SpiceDouble rectan [3]; SpiceDouble r; SpiceDouble slon; SpiceDouble state [6]; /. Load SPK, PCK and LSK kernels, use a meta kernel for convenience. ./ furnsh_c ( "drdsph_ex1.tm" ); /. Look up the apparent state of earth as seen from Mars at January 1, 2005 TDB, relative to the IAU_MARS reference frame. ./ str2et_c ( "January 1, 2005 TDB", &et ); spkezr_c ( "Earth", et, "IAU_MARS", "LT+S", "Mars", state, < ); /. Convert position to spherical coordinates. ./ recsph_c ( state, &r, &colat, &slon ); /. Convert velocity to spherical coordinates. ./ dsphdr_c ( state[0], state[1], state[2], jacobi ); mxv_c ( jacobi, state+3, sphvel ); /. As a check, convert the spherical state back to rectangular coordinates. ./ sphrec_c ( r, colat, slon, rectan ); ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionN.J. Bachman (JPL) J. Diaz del Rio (ODC Space) W.L. Taber (JPL) I.M. Underwood (JPL) ## Version-CSPICE Version 1.1.0, 01-NOV-2021 (JDR) Changed the output argument name "lon" to "slon" for consistency with other routines. Edited the header to comply with NAIF standard. Added complete code example. -CSPICE Version 1.0.0, 19-JUL-2001 (WLT) (IMU) (NJB) ## Index_EntriesJacobian of rectangular w.r.t. spherical coordinates |

Fri Dec 31 18:41:04 2021