Batkhin A.B. Search for Periodic Solutions with Special Symmetry in the Hill Problem

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https://doi.org/10.15688/mpcm.jvolsu.2019.3.1

Batkhin Alexander Borisovich
Candidate of Physical and Mathematical Sciences, Senior Researcher,
Keldysh Institute of Applied Mathematics of Russian Academy of Sciences
This email address is being protected from spambots. You need JavaScript enabled to view it.
https://orcid.org/0000-0001-8871-4697
Miusskaya sq., 4, 125047 Moscow, Russian Federation

Abstract. Nonintegrable classical Hill problem is considered as a variant of a more general problem connecting the Hill problem with integrable Kepler problem in the uniformly rotating frame. We apply the normal form method to the general problem and we obtain so called generating solutions with different types of symmetries. A new class of centrally symmetric generating solutions and the first order approximations to the initial conditions and the period are computed.

Key words: periodic solution, Hill problem, normal form, generating solution, central symmetry.

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Search for Periodic Solutions with Special Symmetry in the Hill Problem by Batkhin A.B. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 22 No. 3 2019, pp. 5-25

 

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