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On the stability of small quasiperiodic motions in the hamiltonian systems

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Abstract

Orbital stability of quasiperiodic motions in the many dimensional autonomic hamiltonian systems is considered. Studied motions are supposed to be not far from equilibrium, the number of their basic frequencies may be not equal to the number of degrees of freedom, and the procedure of their construction is supposed to be converged. The stability problem is solved in the strict nonlinear mode.

Obtained results are used in the stability investigation of small plane motions near the lagrangian solutions of the three-dimensional circular restricted three-body problem. The values of parameters for which the plane motions are unstable have been found.

Резюме

Рассматривается задача орбитальной устойчивости условноперио дических движений в многоменных автономных гамильтоновых системах. Исследуемые движения предполагаются близкими к положению навновесия, число их базисных частот может не совпадать с числом степеней свободы, а процедира их построения считается сходящейся. Задача об устоьчивости решается в строгой нелинейной постановке.

Полученные резильтаты применяются при исследовании устойчивости малых плоских движений, близких лагранжевым решениям пространственной круговой лграниченной задачи трех тел. Найдены значения параметрпв, при которых плоские движения неустойчивы.

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  1. Moscow Aircraft Institute, Moscow, U.S.S.R.

    A. G. Sokolsky

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Sokolsky, A.G. On the stability of small quasiperiodic motions in the hamiltonian systems. Celestial Mechanics 17, 373–394 (1978). https://doi.org/10.1007/BF01228958

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  • DOI: https://doi.org/10.1007/BF01228958

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