drdlat_c |

## Procedurevoid drdlat_c ( SpiceDouble r, SpiceDouble lon, SpiceDouble lat, SpiceDouble jacobi[3][3] ) ## AbstractCompute the Jacobian of the transformation from latitudinal to rectangular coordinates. ## Required_ReadingNone. ## KeywordsCOORDINATES DERIVATIVES MATRIX ## Brief_I/OVariable I/O Description -------- --- -------------------------------------------------- radius 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_Inputradius Distance of a point from the origin. lon Angle of the point from the XZ plane in radians. The angle increases in the counterclockwise sense about the +Z axis. lat 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) ## ExamplesSuppose you have a model that gives radius, longitude, and latitude as functions of time (r(t), lon(t), lat(t)), and that the derivatives (dr/dt, dlon/dt, dlat/dt) are computable. To find the velocity of the object in rectangular coordinates, multiply the Jacobian of the transformation from latitudinal to rectangular (evaluated at r(t), lon(t), lat(t)) by the vector of derivatives of the latitudinal coordinates. This is illustrated by the following code fragment. #include "SpiceUsr.h" . . . /. Load the derivatives of r, lon and lat into the latitudinal velocity vector latv. ./ latv[0] = dr_dt ( t ); latv[1] = dlon_dt ( t ); latv[2] = dlat_dt ( t ); /. Determine the Jacobian of the transformation from latitudinal to rectangular coordinates, using the latitudinal coordinates at time t. ./ ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionW.L. Taber (JPL) N.J. Bachman (JPL) ## Version-CSPICE Version 1.0.0, 20-JUL-2001 (WLT) (NJB) ## Index_EntriesJacobian of rectangular w.r.t. latitudinal coordinates |

Wed Apr 5 17:54:32 2017