Instability of Laplace solutions to the unrestricted three-body problem

Details Instability of Laplace solutions to the unrestricted three-body problem Instability of Laplace solutions to the unrestricted three-body problem

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977pazh....3..376k&link_type=abstract

Pis'ma v Astronomicheskii Zhurnal, vol. 3, Aug. 1977, p. 376-380. In Russian.

Astronomy and Astrophysics

Astronomy

1

Laplace Equation, Motion Stability, Orbital Mechanics, Three Body Problem, Liapunov Functions, Perturbation, Resonance

Scientific paper

Methods taken from internal-resonance theory are used to analyze the stability of Laplace solutions to the unrestricted three-body problem on all third-order resonance curves. Steady Laplace motions of the three bodies are considered in which all three points are located at the vertices of a fixed equilateral triangle rotating uniformly about its center of mass. Liapunov's (1954) variables and equations are employed to obtain the equations of perturbed motion. It is shown that in the region where the Routh-Zhukovsky stability conditions are satisfied to the first approximation, there exists a 'resonance' set of masses of the three bodies for which Laplace solutions to the unrestricted three-body problem are strictly unstable in the sense of Liapunov.

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