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arXiv · 1112.0733

Large Lagrangian Actions on Elliptical Solutions of 2-Body and 3-Body Problems with Fixed Energies

Ying Lv·Shiqing Zhang
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Abstract

Based on the works of Gordon ([4]) and Zhang-Zhou([8])) 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-Coti Zelati ([1]) to compute the Lagrangian actions on Keplerian and Lagrangian elliptical solutions with fixed energies, we also find an interesting relationship between period and energy for Lagrangian elliptical solutions with Newtonian potentials.

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Ying Lv, Shiqing Zhang. 2011-12-04. Large Lagrangian Actions on Elliptical Solutions of 2-Body and 3-Body Problems with Fixed Energies. https://arxiv.org/abs/1112.0733

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