Large Lagrangian Actions on Elliptical Solutions of 2-Body and 3-Body Problems with Fixed Energies
Mathematical Physics
2011-12-06 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1112.0733,
title = {Large Lagrangian Actions on Elliptical Solutions of 2-Body and 3-Body Problems with Fixed Energies},
author = {Ying Lv and Shiqing Zhang},
journal= {arXiv preprint arXiv:1112.0733},
year = {2011}
}