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Preprints of the Keldysh Institute of Applied Mathematics, 2005, 010
(Mi ipmp651)
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On families of periodic solutions to the restricted three-body problem
A. D. Bruno, V. P. Varin
Abstract:
We consider the plane circular restricted three-body problem. It is described by the autonomous Hamiltonian system with two degrees of freedom and one small parameter $\mu\in[0,1/2]$ which is the mass ratio of the two massive bodies. Periodic solutions to this problem form two-parameter families. We propose methods of computation of symmetric periodic solutions for all values of parameter $\mu$. Each solution has period and two traces, namely, the plane and the vertical one. Two characteristics of a family, i.e. its intersection with the symmetry plane, are plotted in the three coordinate systems: one global and two local ones related to the two massive bodies. We also describe generating families, i.e. the limits of families as $\mu\to0$, which are known explicitly.
Citation:
A. D. Bruno, V. P. Varin, “On families of periodic solutions to the restricted three-body problem”, Keldysh Institute preprints, 2005, 010
Linking options:
https://www.mathnet.ru/eng/ipmp651 https://www.mathnet.ru/eng/ipmp/y2005/p10
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Statistics & downloads: |
Abstract page: | 95 | Full-text PDF : | 14 |
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