dsphdr_c |

Table of contents## Proceduredsphdr_c ( Derivative of spherical w.r.t. rectangular ) void dsphdr_c ( SpiceDouble x, SpiceDouble y, SpiceDouble z, SpiceDouble jacobi[3][3] ) ## AbstractCompute the Jacobian matrix of the transformation from rectangular to spherical coordinates. ## Required_ReadingNone. ## KeywordsCOORDINATES DERIVATIVES MATRIX ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- x I x-coordinate of point. y I y-coordinate of point. z I z-coordinate of point. jacobi O Matrix of partial derivatives. ## Detailed_Inputx, y, z are the rectangular coordinates of the point at which the Jacobian of the map from rectangular to spherical coordinates is desired. ## Detailed_Outputjacobi is the matrix of partial derivatives of the conversion between rectangular and spherical coordinates. It has the form .- -. | dr/dx dr/dy dr/dz | | dcolat/dx dcolat/dy dcolat/dz | | dlon/dx dlon/dy dlon/dz | `- -' evaluated at the input values of x, y, and z. ## ParametersNone. ## Exceptions1) If the input point is on the z-axis (x and y = 0), the Jacobian is undefined, the error SPICE(POINTONZAXIS) is signaled by a routine in the call tree of this routine. ## FilesNone. ## 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 spherical coordinates to gain insights about phenomena in this coordinate frame. To transform rectangular velocities to derivatives of coordinates in a spherical 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 corresponding spherical coordinate derivatives are given by the matrix equation: t | t (dr, dcolat, dlon) = jacobi| * (dx, dy, dz) |(x,y,z) This routine computes the matrix | jacobi| |(x, y, z) ## 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: dsphdr_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 dsphdr_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 ( "dsphdr_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. ./ ## 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, 01-NOV-2021 (JDR) Edited the header to comply with NAIF standard. Added complete code example. -CSPICE Version 1.0.0, 20-JUL-2001 (WLT) (NJB) ## Index_EntriesJacobian of spherical w.r.t. rectangular coordinates |

Fri Dec 31 18:41:05 2021