Journal
APPLIED MATHEMATICS LETTERS
Volume 83, Issue -, Pages 15-20Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2018.03.009
Keywords
2 and 3-body problems; Keplerian orbits; Lagrangian solutions; Fixed energy; Lagrangian actions
Categories
Funding
- NSFC [11601438, 11671278]
- NSF of China
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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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