dsphdr_c |

## Procedurevoid dsphdr_c ( SpiceDouble x, SpiceDouble y, SpiceDouble z, SpiceDouble jacobi[3][3] ) ## AbstractThis routine computes the Jacobian 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) will be signaled. ## 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) ## ExamplesSuppose one is given the bodyfixed rectangular state of an object (x(t), y(t), z(t), dx(t), dy(t), dz(t)) as a function of time t. To find the derivatives of the coordinates of the object in bodyfixed spherical coordinates, one simply multiplies the Jacobian of the transformation from rectangular to spherical coordinates (evaluated at x(t), y(t), z(t)) by the rectangular velocity vector of the object at time t. In code this looks like: #include "SpiceUsr.h" . . . /. Load the rectangular velocity vector vector recv. ./ recv[0] = dx ( t ); recv[1] = dy ( t ); recv[2] = dz ( t ); /. Determine the Jacobian of the transformation from rectangular to spherical coordinates at the rectangular 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 spherical w.r.t. rectangular coordinates |

Wed Apr 5 17:54:32 2017