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: http://www.stsci.edu/~sontag/spicedocs/cspice/dvdot_c.html
Дата изменения: Sat Dec 17 06:08:47 2005 Дата индексирования: Sun Apr 10 23:24:42 2016 Кодировка: Поисковые слова: cosmic rays |
Compute the derivative of the dot product of two double precision position vectors.
None.
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>
s1 Any state vector. The components are in order (x, y, z, dx/dt, dy/dt, dz/dt ) s2 Any state vector.
The function returns the derivative of the dot product of the position portions of the two state vectors s1 and s2.
None.
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.
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.
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.
Error free.
None.
W.L. Taber (JPL) E.D. Wright (JPL)
None.
-CSPICE Version 1.0.0, 7-JUL-1999
Compute the derivative of a dot product