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

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.

preprint2011arXivOpen access
Ying LvShiqing Zhang
math-phmath.MP
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Ying LvShiqing Zhang

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