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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_DVDOT returns the time derivative of the dot product of
   two position vectors.

I/O


   Given:

      s1   a SPICE state(s);

              s1 = (r1, dr1 ).
                         --
                         dt

           [6,n] = size(s1); double = class(s1)

      s2   a second SPICE state(s);

              s2 = (r2, dr2 ).
                        --
                        dt

           [6,n] = size(s2); double = class(s2)

      An implicit assumption exists that 's1' and 's2' are specified
      in the same reference frame. If this is not the case, the numerical
      result has no meaning.

   the call:

      dvdot = cspice_dvdot( s1, s2 )

   returns:

      dvdot   the time derivative(s) of the dot product between the position
              components of 's1' and 's2'.

              'dvdot' returns with the same vectorization measure (N)
              as 's1' and 's2'.

              [1,n] = size(dvdot); double = class(dvdot)

Examples


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

     Suppose that given two state vectors (s1 and s2) whose position
     components are unit vectors, and that we need to compute the
     rate of change of the angle between the two vectors.

     We know that the Cosine of the angle THETA between them is given
     by

        cos(theta) = dot(s1,s2)

     Thus by the chain rule, the derivative of the angle is given
     by:

        sine(theta) dtheta/dt = cspice_dvdot(s1,s2)

     Thus for values of theta away from zero we can compute

     dtheta/dt as

     dtheta = cspice_dvdot(s1,s2) / sqrt( 1 - dot(s1,s2)**2 )

     Note that position components of s1 and s2 are parallel, the
     derivative of the  angle between the positions does not
     exist.  Any code that computes the derivative of the angle
     between two position vectors should account for the case
     when the position components are parallel.

Particulars


   In this discussion, the notation

      < V1, V2 >

   indicates the dot product of vectors V1 and V2.

   Given two state vectors s1 and s2 made up of position and velocity
   components (r1,v1) and (r2,v2) respectively, cspice_dvdot calculates
   the derivative of the dot product of p1 and p2, i.e. the time
   derivative

         d
         -- < r1, r2 > = < v1, r2 > + < r1, v2 >
         dt

Required Reading


   For important details concerning this module's function, please refer to
   the CSPICE routine dvdot_c.

   MICE.REQ

Version


   -Mice Version 1.0.0, 20-APR-2010, EDW (JPL)

Index_Entries


   time derivative of a dot product


Wed Apr  5 18:00:31 2017