drdgeo_c |

## Procedurevoid drdgeo_c ( SpiceDouble lon, SpiceDouble lat, SpiceDouble alt, SpiceDouble re, SpiceDouble f, SpiceDouble jacobi[3][3] ) ## AbstractThis routine computes the Jacobian of the transformation from geodetic to rectangular coordinates. ## Required_ReadingNone. ## KeywordsCOORDINATES DERIVATIVES MATRIX ## Brief_I/OVariable I/O Description -------- --- -------------------------------------------------- lon I Geodetic longitude of point (radians). lat I Geodetic latitude of point (radians). alt I Altitude of point above the reference spheroid. re I Equatorial radius of the reference spheroid. f I Flattening coefficient. jacobi O Matrix of partial derivatives. ## Detailed_Inputlon Geodetic longitude of point (radians). lat Geodetic latitude of point (radians). alt Altitude of point above the reference spheroid. 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 geodetic and rectangular coordinates. It has the form .- -. | dx/dlon dx/dlat dx/dalt | | dy/dlon dy/dlat dy/dalt | | dz/dlon dz/dlat dz/dalt | `- -' evaluated at the input values of lon, lat and alt. The formulae for computing x, y, and z from geodetic coordinates are given below. x = [alt + re/g(lat,f)]*cos(lon)*cos(lat) y = [alt + re/g(lat,f)]*sin(lon)*cos(lat) 2 z = [alt + re*(1-f) /g(lat,f)]* sin(lat) where re is the polar radius of the reference spheroid. f is the flattening factor (the polar radius is obtained by multiplying the equatorial radius by 1-f). g( lat, f ) is given by 2 2 2 sqrt ( cos (lat) + (1-f) * sin (lat) ) ## ParametersNone. ## Exceptions1) If the flattening coefficient is greater than or equal to one, the error SPICE(VALUEOUTOFRANGE) is signaled. 2) If the equatorial radius is non-positive, the error SPICE(BADRADIUS) is signaled. ## FilesNone. ## ParticularsIt is often convenient to describe the motion of an object in the geodetic coordinate system. However, when performing vector computations its hard to beat rectangular coordinates. To transform states given with respect to geodetic coordinates to states with respect to rectangular coordinates, one makes use of the Jacobian of the transformation between the two systems. Given a state in geodetic coordinates ( lon, lat, alt, dlon, dlat, dalt ) the velocity in rectangular coordinates is given by the matrix equation: t | t (dx, dy, dz) = jacobi| * (dlon, dlat, dalt) |(lon,lat,alt) This routine computes the matrix | jacobi| |(lon,lat,alt) ## ExamplesSuppose that one has a model that gives radius, longitude and latitude as a function of time (lon(t), lat(t), alt(t) ) for which the derivatives ( dlon/dt, dlat/dt, dalt/dt ) are computable. To find the velocity of the object in bodyfixed rectangular coordinates, one simply multiplies the Jacobian of the transformation from geodetic to rectangular coordinates, evaluated at (lon(t), lat(t), alt(t) ), by the vector of derivatives of the geodetic coordinates. In code this looks like: #include "SpiceUsr.h" . . . /. Load the derivatives of lon, lat, and alt into the geodetic velocity vector GEOV. ./ geov[0] = dlon_dt ( t ); geov[1] = dlat_dt ( t ); geov[2] = dalt_dt ( t ); /. Determine the Jacobian of the transformation from geodetic to rectangular coordinates at the geodetic coordinates of 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. geodetic coordinates |

Wed Apr 5 17:54:32 2017