Computer program analyzes the motion of two rigid bodies in space, separating as a result of any one, or a combination of, the following mechanisms - springs with ball ends, springs with one end guided, pyrotechnics, rockets, cold-gas jets, air pistons, and Coulomb drag

Chamberlain, R. G.

Mack, T. H.

Silsby, W.

English

NASA Technical Reports Server

December 1970	 Brief 70-10625 
.
NASA TECH BRIEF 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage commercial 
application. Tech Briefs are available on a subscription basis from the National Technical Information Service, Springfield, 
Virginia 22151. Requests for individual copies or questions relating to the Tech Brief progam may be directed to the Tech-
nology Utilization Division, NASA, Code UT, Washington, D.C. 20546. 
Separation of Two Bodies in Space 
The problem: 
To develop an automated analytical tool for solving 
problems of two-body separation in space. 
The solution: 
A computer program for the motion of two rigid 
bodies in space, separating as a result of any one,or a 
combination of, the following force mechanisms: 
springs with ball ends, springs with one end guided, 
pyrotechnics, rockets, cold-gas jets, air pistons, and 
coulomb drag. 
How it's done: 
The basic approach to the problem is a straight-
forward application of the Lagrange equations, aug-
mented by undetermined multipliers. The mathe-
matical complexity of the resultant equations is pri-
marily due to the large number of degrees of freedom 
(12) and the coordinate transformations involved. 
The forces arising from the various mechanisms are 
represented by mathematical models. The models as-
sume two rigid bodies subjected to the action of 
forces from the following types of idealized devices: 
linear springs hard mounted on one body and bearing 
on the other. (either with frictionless slippage or no 
slippage); linear springs between the two bodies,with 
universal joints at both ends; pryotechnic devices 
applying impulsive forces; cold-gas jets - adiabatic 
processes of an ideal gas; pneumatic pistons - adia-
batic processes of an ideal gas; coulomb drag between 
the bodies; and rockets (constant force), including 
linear changes in inertia properties. 
The primary assumptions concerning the forces are 
implicitly contained in the descriptions of these 
idealized devices. It has been assumed that the bodies
do not have separation distances that are significant 
relative to the distance from the common center of 
mass (CM) to the center of any external force-field. 
The equations of. motion are written in a reference 
•frame that has fixed directions in inertial space but 
moves with the pre-separation trajectory of the two 
bodies; this frame is assumed to be inertial. The 
results are then correct (when used in combination 
with a trajectory solution for the common CM) if there 
are no forces acting other than the ones considered in 
the analysis, or if there is an external force-field 
exerting approximately the same vector force per unit 
mass on each element of the system. 
No approximations are used in the derivation of the 
classical equationsof motion; they are numerically 
integrated by the Adams-Moulton method. 
Notes: 
I. The program is written in FORTRAN 11 and FAP 
for use on the IBM 7094 computer. The SC 4020 
plotter is also used in plotting a part of the out-
put. 
2. Inquiries may be directed to: 
COSMIC 
Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: B70-10625 
Source: T.H. Mack, R.G. Chamberlain and W. Silsby

Caltech/JPL
under contract to

NASA Pasadena Office

(NPO- 10663)
Category 09 
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Separation of two bodies in space

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