Stability of periodic motions close to the Lagrangian solutions

Details Stability of periodic motions close to the Lagrangian solutions Stability of periodic motions close to the Lagrangian solutions

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977azh....54..897m&link_type=abstract

Astronomicheskii Zhurnal, vol. 54, July-Aug. 1977, p. 897-908. In Russian.

Astronomy and Astrophysics

Astronomy

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.

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