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Regular and Chaotic Dynamics, 2021, Volume 26, Issue 4, Pages 439–455
DOI: https://doi.org/10.1134/S1560354721040079 (Mi rcd1124) 		 
Nonintegrability of the Reduced Planar Three-body Problem with Generalized Force

Mitsuru Shibayama, Junji Yamada

Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, 606-8501 Kyoto, Japan
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DOI: https://doi.org/10.1134/S1560354721040079
Abstract: We consider the planar three-body problem with generalized potentials. Some nonintegrability results for these systems have been obtained by analyzing the variational equations along homothetic solutions. But we cannot apply it to several exceptional cases. For example, in the case of inverse-square potentials, the variational equations along homothetic solutions are solvable. We obtain sufficient conditions for nonintegrability for these exceptional cases by focusing on some particular solutions that are different from homothetic solutions.
Keywords: nonintegrability, three-body problem.
Funding agency Grant number
Japan Society for the Promotion of Science 18K03366
M. S. is supported by the Japanese Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research (C) No. 18K03366.
Received: 24.01.2021
Accepted: 30.05.2021
Bibliographic databases:
Document Type: Article
MSC: 70H07, 70F07 (37J30, 34M15)
Language: English
Citation: Mitsuru Shibayama, Junji Yamada, “Nonintegrability of the Reduced Planar Three-body Problem with Generalized Force”, Regul. Chaotic Dyn., 26:4 (2021), 439–455
Citation in format AMSBIB
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\by Mitsuru Shibayama, Junji Yamada
\paper Nonintegrability of the Reduced Planar Three-body Problem
with Generalized Force
\jour Regul. Chaotic Dyn.
\yr 2021
\vol 26
\issue 4
\pages 439--455
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\crossref{https://doi.org/10.1134/S1560354721040079}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85112164886}
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