1 /* dvdot.f -- translated by f2c (version 19980913).
2 You must link the resulting object file with the libraries:
3 -lf2c -lm (in that order)
4 */
5
6 #include "f2c.h"
7
8 /* $Procedure DVDOT ( Derivative of Vector Dot Product, 3-D ) */
dvdot_(doublereal * s1,doublereal * s2)9 doublereal dvdot_(doublereal *s1, doublereal *s2)
10 {
11 /* System generated locals */
12 doublereal ret_val;
13
14 /* $ Abstract */
15
16 /* Compute the derivative of the dot product of two double */
17 /* precision position vectors. */
18
19 /* $ Disclaimer */
20
21 /* THIS SOFTWARE AND ANY RELATED MATERIALS WERE CREATED BY THE */
22 /* CALIFORNIA INSTITUTE OF TECHNOLOGY (CALTECH) UNDER A U.S. */
23 /* GOVERNMENT CONTRACT WITH THE NATIONAL AERONAUTICS AND SPACE */
24 /* ADMINISTRATION (NASA). THE SOFTWARE IS TECHNOLOGY AND SOFTWARE */
25 /* PUBLICLY AVAILABLE UNDER U.S. EXPORT LAWS AND IS PROVIDED "AS-IS" */
26 /* TO THE RECIPIENT WITHOUT WARRANTY OF ANY KIND, INCLUDING ANY */
27 /* WARRANTIES OF PERFORMANCE OR MERCHANTABILITY OR FITNESS FOR A */
28 /* PARTICULAR USE OR PURPOSE (AS SET FORTH IN UNITED STATES UCC */
29 /* SECTIONS 2312-2313) OR FOR ANY PURPOSE WHATSOEVER, FOR THE */
30 /* SOFTWARE AND RELATED MATERIALS, HOWEVER USED. */
31
32 /* IN NO EVENT SHALL CALTECH, ITS JET PROPULSION LABORATORY, OR NASA */
33 /* BE LIABLE FOR ANY DAMAGES AND/OR COSTS, INCLUDING, BUT NOT */
34 /* LIMITED TO, INCIDENTAL OR CONSEQUENTIAL DAMAGES OF ANY KIND, */
35 /* INCLUDING ECONOMIC DAMAGE OR INJURY TO PROPERTY AND LOST PROFITS, */
36 /* REGARDLESS OF WHETHER CALTECH, JPL, OR NASA BE ADVISED, HAVE */
37 /* REASON TO KNOW, OR, IN FACT, SHALL KNOW OF THE POSSIBILITY. */
38
39 /* RECIPIENT BEARS ALL RISK RELATING TO QUALITY AND PERFORMANCE OF */
40 /* THE SOFTWARE AND ANY RELATED MATERIALS, AND AGREES TO INDEMNIFY */
41 /* CALTECH AND NASA FOR ALL THIRD-PARTY CLAIMS RESULTING FROM THE */
42 /* ACTIONS OF RECIPIENT IN THE USE OF THE SOFTWARE. */
43
44 /* $ Required_Reading */
45
46 /* None. */
47
48 /* $ Keywords */
49
50 /* VECTOR */
51 /* DERIVATIVE */
52
53 /* $ Declarations */
54 /* $ Brief_I/O */
55
56 /* VARIABLE I/O DESCRIPTION */
57 /* -------- --- -------------------------------------------------- */
58 /* S1 I First state vector in the dot product. */
59 /* S2 I Second state vector in the dot product. */
60
61 /* The function returns the derivative of the dot product <S1,S2> */
62
63 /* $ Detailed_Input */
64
65 /* S1 Any state vector. The componets are in order */
66 /* (x, y, z, dx/dt, dy/dt, dz/dt ) */
67
68 /* S2 Any state vector. */
69
70 /* $ Detailed_Output */
71
72 /* The function returns the derivative of the dot product of the */
73 /* position portions of the two state vectors S1 and S2. */
74
75 /* $ Parameters */
76
77 /* None. */
78
79 /* $ Files */
80
81 /* None. */
82
83 /* $ Exceptions */
84
85 /* Error free. */
86
87 /* $ Particulars */
88
89 /* Given two state vectors S1 and S2 made up of position and */
90 /* velocity components (P1,V1) and (P2,V2) respectively, */
91 /* DVDOT calculates the derivative of the dot product of P1 and P2, */
92 /* i.e. the time derivative */
93
94 /* d */
95 /* -- < P1, P2 > = < V1, P2 > + < P1, V2 > */
96 /* dt */
97
98 /* where <,> denotes the dot product operation. */
99
100 /* $ Examples */
101
102 /* Suppose that given two state vectors (S1 and S2)whose position */
103 /* components are unit vectors, and that we need to compute the */
104 /* rate of change of the angle between the two vectors. */
105
106 /* We know that the Cosine of the angle THETA between them is given */
107 /* by */
108
109 /* COSINE(THETA) = VDOT(S1,S2) */
110
111 /* Thus by the chain rule, the derivative of the angle is given */
112 /* by: */
113
114 /* SINE(THETA) dTHETA/dt = DVDOT(S1,S2) */
115
116 /* Thus for values of THETA away from zero we can compute */
117
118 /* dTHETA/dt as */
119
120 /* DTHETA = DVDOT(S1,S2) / SQRT ( 1 - VDOT(S1,S2)**2 ) */
121
122 /* Note that position components of S1 and S2 are parallel, the */
123 /* derivative of the angle between the positions does not */
124 /* exist. Any code that computes the derivative of the angle */
125 /* between two position vectors should account for the case */
126 /* when the position components are parallel. */
127
128 /* $ Restrictions */
129
130 /* The user is responsible for determining that the states S1 and */
131 /* S2 are not so large as to cause numeric overflow. In most cases */
132 /* this won't present a problem. */
133
134 /* $ Author_and_Institution */
135
136 /* W.L. Taber (JPL) */
137
138 /* $ Literature_References */
139
140 /* None. */
141
142 /* $ Version */
143
144 /* - SPICELIB Version 1.0.0, 18-MAY-1995 (WLT) */
145
146
147 /* -& */
148 /* $ Index_Entries */
149
150 /* Compute the derivative of a dot product */
151
152 /* -& */
153
154 ret_val = s1[0] * s2[3] + s1[1] * s2[4] + s1[2] * s2[5] + s1[3] * s2[0] +
155 s1[4] * s2[1] + s1[5] * s2[2];
156 return ret_val;
157 } /* dvdot_ */
158
159