dgeodr_c |

## Procedurevoid dgeodr_c ( SpiceDouble x, SpiceDouble y, SpiceDouble z, SpiceDouble re, SpiceDouble f, SpiceDouble jacobi[3][3] ) ## AbstractThis routine computes the Jacobian of the transformation from rectangular to geodetic 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. RE I Equatorial radius of the reference spheroid. F I Flattening coefficient. 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 geodetic coordinates is desired. re Equatorial radius of the reference spheroid. f Flattening coefficient = (re-rp) / re, where rp is the polar radius of the spheroid. (More importantly rp = re*(1-f).) ## Detailed_Outputjacobi is the matrix of partial derivatives of the conversion between rectangular and geodetic coordinates. It has the form .- -. | dlon/dx dlon/dy dlon/dz | | dlat/dx dlat/dy dlat/dz | | dalt/dx dalt/dy dalt/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. 2) If the flattening coefficient is greater than or equal to one, the error SPICE(VALUEOUTOFRANGE) is signaled. 3) If the equatorial radius is not positive, the error SPICE(BADRADIUS) is 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 geodetic coordinates to gain insights about phenomena in this coordinate frame. To transform rectangular velocities to derivatives of coordinates in a geodetic 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 velocity in geodetic coordinates is given by the matrix equation: t | t (dlon, dlat, dalt) = 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 geodetic coordinates, one simply multiplies the Jacobian of the transformation from rectangular to geodetic 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_dt ( t ); recv[1] = dy_dt ( t ); recv[2] = dz_dt ( t ); /. Determine the Jacobian of the transformation from rectangular to geodetic 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, 18-JUL-2001 (WLT) (NJB) ## Index_EntriesJacobian of geodetic w.r.t. rectangular coordinates |

Wed Apr 5 17:54:31 2017