Index Page dvdot_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       SpiceDouble dvdot_c ( ConstSpiceDouble s1[6],
                             ConstSpiceDouble s2[6] )

#### Abstract

       Compute the derivative of the dot product of two double
       precision position vectors.

#### Required_Reading

       None.

#### Keywords

       VECTOR
       DERIVATIVE

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       s1         I   First state vector in the dot product.
       s2         I   Second state vector in the dot product.

       The function returns the derivative of the dot product <s1,s2>

#### Detailed_Input

       s1      Any state vector.  The components are in order
               (x, y, z, dx/dt, dy/dt, dz/dt )

       s2      Any state vector.

#### Detailed_Output

       The function returns the derivative of the dot product of the
       position portions of the two state vectors s1 and s2.

#### Parameters

       None.

#### Exceptions

       Error free.

#### Files

       None.

#### Particulars

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

             d
             -- < p1, p2 > = < v1, p2 > + < p1, v2 >
             dt

       where <,> denotes the dot product operation.

#### Examples

       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 the vectors is
       given by

          cosine(theta) = vdot_c(s1,s2)

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

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

       Thus for values of theta away from zero we can compute

       dtheta/dt as

       dtheta = dvdot_c(s1,s2) / sqrt ( 1 - vdot_c(s1,s2)**2 )

       Note if the 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.

#### Restrictions

       The user is responsible for determining that the states s1 and
       s2 are not so large as to cause numeric overflow.  In most cases
       this won't present a problem.

#### Literature_References

       None.

#### Author_and_Institution

       W.L. Taber      (JPL)
       E.D. Wright     (JPL)

#### Version

       -CSPICE Version 1.0.0, 7-JUL-1999

#### Index_Entries

       Compute the derivative of a dot product

#### Link to routine dvdot_c source file dvdot_c.c

    Wed Apr  5 17:54:33 2017