drdcyl_c |

## Procedurevoid drdcyl_c ( SpiceDouble r, SpiceDouble lon, SpiceDouble z, SpiceDouble jacobi[3][3] ) ## AbstractThis routine computes the Jacobian of the transformation from cylindrical 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. z I Height of the point above the xy plane. jacobi O Matrix of partial derivatives. ## Detailed_Inputr Distance of the point of interest from z axis. lon Cylindrical angle (in radians) of the point of interest from xz plane. The angle increases in the counterclockwise sense about the +z axis. z Height of the point above xy plane. ## Detailed_Outputjacobi is the matrix of partial derivatives of the conversion between cylindrical and rectangular coordinates. It has the form .- -. | dx/dr dx/dlon dx/dz | | | | dy/dr dy/dlon dy/dz | | | | dz/dr dz/dlon dz/dz | `- -' evaluated at the input values of r, lon and z. Here x,y, and z are given by the familiar formulae x = r*cos(lon) y = r*sin(lon) z = z ## ParametersNone. ## ExceptionsError free. ## FilesNone. ## ParticularsIt is often convenient to describe the motion of an object in the cylindrical coordinate system. However, when performing vector computations its hard to beat rectangular coordinates. To transform states given with respect to cylindrical coordinates to states with respect to rectangular coordinates, one uses the Jacobian of the transformation between the two systems. Given a state in cylindrical coordinates ( r, lon, z, dr, dlon, dz ) the velocity in rectangular coordinates is given by the matrix equation: t | t (dx, dy, dz) = jacobi| * (dr, dlon, dz) |(r,lon,z) This routine computes the matrix | jacobi| |(r,lon,z) ## ExamplesSuppose that one has a model that gives radius, longitude and height as a function of time (r(t), lon(t), z(t)) for which the derivatives ( dr/dt, dlon/dt, dz/dt ) are computable. To find the corresponing velocity in bodyfixed rectangular coordinates, one simply multiplies the Jacobian of the transformation from cylindrical to rectangular coordinates (evaluated at r(t), lon(t), z(t) ) by the vector of derivatives of the cylindrical coordinates. In code this looks like: #include "SpiceUsr.h" . . . /. Load the derivatives of r, lon, and z into the cylindrical velocity vector sphv. ./ cylv[0] = dr_dt ( t ); cylv[1] = dlon_dt ( t ); cylv[2] = dz_dt ( t ); /. Determine the Jacobian of the transformation from cylindrical to rectangular at the coordinates at the given cylindrical coordinates at time t. ./ ## RestrictionsNone. ## Literature_ReferencesNone. ## Author_and_InstitutionW.L. Taber (JPL) I.M. Underwood (JPL) N.J. Bachman (JPL) ## Version-CSPICE Version 1.0.0, 19-JUL-2001 (WLT) (IMU) (NJB) ## Index_EntriesJacobian of rectangular w.r.t. cylindrical coordinates |

Wed Apr 5 17:54:32 2017