期刊
APPLIED MATHEMATICS LETTERS
卷 83, 期 -, 页码 15-20出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2018.03.009
关键词
2 and 3-body problems; Keplerian orbits; Lagrangian solutions; Fixed energy; Lagrangian actions
资金
- NSFC [11601438, 11671278]
- NSF of China
Based on the works of Gordon (1977) and Zhang and Zhou (2001) on the variational minimizing properties for Keplerian orbits and Lagrangian solutions of Newtonian 2-body and 3-body problems, we use the constrained variational principle of Ambrosetti and Coti Zelati (1990) to compute the Lagrangian actions on Keplerian and Lagrangian elliptical solutions with fixed energies. We also find an interesting relation between the period and the energy for Lagrangian elliptical solutions with Newtonian potentials. (C) 2018 Elsevier Ltd. All rights reserved.
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