The eleventh motion constant of the two-body problem |
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| Authors: | Andrew J Sinclair John E Hurtado |
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| Institution: | 1.Aerospace Engineering Department,Auburn University,Auburn,USA;2.Aerospace Engineering Department,Texas A&M University,College Station,USA |
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| Abstract: | The two-body problem is a twelfth-order time-invariant dynamic system, and therefore has eleven mutually-independent time-independent
integrals, here referred to as motion constants. Some of these motion constants are related to the ten mutually-independent
algebraic integrals of the n-body problem, whereas some are particular to the two-body problem. The problem can be decomposed into mass-center and relative-motion
subsystems, each being sixth-order and each having five mutually-independent motion constants. This paper presents solutions
for the eleventh motion constant, which relates the behavior of the two subsystems. The complete set of mutually-independent
motion constants describes the shape of the state-space trajectories. The use of the eleventh motion constant is demonstrated
in computing a solution to a two-point boundary-value problem. |
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