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

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

2011-12-04

arxiv.org/abs/1112.0733v1

Physics

Mathematical Physics

Scientific paper

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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