The eleventh motion constant of the two-body problem Academic Article

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. 2011 Springer Science+Business Media B.V.

authors

• Hurtado, John

published proceedings

• CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY

author list (cited authors)

• Sinclair, A. J., & Hurtado, J. E.

citation count

• 1

publication date

• July 2011

publisher

• Springer Nature  Publisher

keywords

• Boundary-value Problems
• Motion Constants
• Two-body Problem

Digital Object Identifier (DOI)

• 10.1007/s10569-011-9350-6

start page

• 189

end page

• 198

volume

• 110

issue

• 3

URL

• http://dx.doi.org/10.1007/s10569-011-9350-6