Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977sva....21..507m&link_type=abstract
(Astronomicheskii Zhurnal, vol. 54, July-Aug. 1977, p. 897-908.) Soviet Astronomy, vol. 21, July-Aug. 1977, p. 507-512. Transla
Astronomy and Astrophysics
Astronomy
1
Lagrangian Equilibrium Points, Motion Stability, Orbital Mechanics, Three Body Problem, Graph Theory, Hamiltonian Functions, Normalizing, Periodic Functions, Resonance
Scientific paper
The problem of the orbital stability of small periodic motions close to the Lagrangian solutions of the two-dimensional and three-dimensional circular restricted three-body problems is solved in a nonlinear formulation. From Liapunov's theorem on holomorphic intervals it follows that three types of periodic solutions exist for the canonical system of differential equations with Hamiltonian in the form of a series. This paper investigates the stability of type I motions in the plane and in space, type II motions in the plane and space, and type III motions in space. Normalization of the Hamiltonian for perturbed motion was done with the aid of Markeev's (1976) algorithms on computer. It was found sufficient to retain fourth-order terms in the initial Hamiltonian for most nonresonant cases.
Markeev Anatoliy P.
Sokolskii A. G.
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