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

2011/12/04 by Ying Lv, Lv, Ying, Shiqing Zhang +1
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Spacecraft Dynamics and Control #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1112.0733

arxiv created 2011/12/04 · openalex publication_date 2011/12/04 · arxiv updated 2011/12/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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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