drdlat_c |

Table of contents## Proceduredrdlat_c ( Derivative of rectangular w.r.t. latitudinal ) void drdlat_c ( SpiceDouble r, SpiceDouble lon, SpiceDouble lat, SpiceDouble jacobi[3][3] ) ## AbstractCompute the Jacobian matrix of the transformation from latitudinal to rectangular coordinates. ## Required_ReadingNone. ## KeywordsCOORDINATES DERIVATIVES MATRIX ## Brief_I/OVARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- r I Distance of a point from the origin. lon I Angle of the point from the XZ plane in radians. lat I Angle of the point from the XY plane in radians. jacobi O Matrix of partial derivatives. ## Detailed_Inputr is the distance of a point from the origin. lon is the angle of the point from the XZ plane in radians. The angle increases in the counterclockwise sense about the +Z axis. lat is the angle of the point from the XY plane in radians. The angle increases in the direction of the +Z axis. ## Detailed_Outputjacobi is the matrix of partial derivatives of the conversion between latitudinal and rectangular coordinates. It has the form .- -. | dx/dr dx/dlon dx/dlat | | | | dy/dr dy/dlon dy/dlat | | | | dz/dr dz/dlon dz/dlat | `- -' evaluated at the input values of r, lon and lat. Here x, y, and z are given by the familiar formulae x = r * cos(lon) * cos(lat) y = r * sin(lon) * cos(lat) z = r * sin(lat). ## ParametersNone. ## ExceptionsError free. ## FilesNone. ## ParticularsIt is often convenient to describe the motion of an object in latitudinal coordinates. It is also convenient to manipulate vectors associated with the object in rectangular coordinates. The transformation of a latitudinal state into an equivalent rectangular state makes use of the Jacobian of the transformation between the two systems. Given a state in latitudinal coordinates, ( r, lon, lat, dr, dlon, dlat ) the velocity in rectangular coordinates is given by the matrix equation t | t (dx, dy, dz) = jacobi| * (dr, dlon, dlat) |(r,lon,lat) This routine computes the matrix | jacobi| |(r,lon,lat) ## 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 latitudinal 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: drdlat_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 drdlat_ex1 ./ #include <stdio.h> #include "SpiceUsr.h" int main( ) { /. Local variables ./ SpiceDouble drectn [3]; SpiceDouble et; SpiceDouble jacobi [3][3]; SpiceDouble lat; SpiceDouble lon; SpiceDouble lt; SpiceDouble latvel [3]; SpiceDouble rectan [3]; SpiceDouble r; SpiceDouble state [6]; /. Load SPK, PCK and LSK kernels, use a meta kernel for convenience. ./ furnsh_c ( "drdlat_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 latitudinal coordinates. ./ reclat_c ( state, &r, &lon, &lat ); /. Convert velocity to latitudinal coordinates. ./ dlatdr_c ( state[0], state[1], state[2], jacobi ); mxv_c ( jacobi, state+3, latvel ); /. As a check, convert the latitudinal state back to rectangular coordinates. ./ latrec_c ( r, lon, lat, rectan ); ## 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. Updated -Brief_I/O and -Detailed_Input sections to correct `r' argument name, which in previous version was `radius'. -CSPICE Version 1.0.0, 20-JUL-2001 (WLT) (NJB) ## Index_EntriesJacobian of rectangular w.r.t. latitudinal coordinates |

Fri Dec 31 18:41:04 2021