Keplerian Action, Convexity Optimization, and the 4-Body Problem

Year:    2021

Author:    Kuo-Chang Chen

Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 24–58

Abstract

In this paper we introduce a method to construct periodic solutions for the $n$-body problem with only boundary and topological constraints. Our approach is based on some novel features of the Keplerian action functional, constraint convex optimization techniques, and variational methods. We demonstrate the strength of this method by constructing relative periodic solutions for the planar four-body problem within a special topological class, and our results hold for an open set of masses.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2021.pr80.04

Analysis in Theory and Applications, Vol. 37 (2021), Iss. 1 : pp. 24–58

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    35

Keywords:    $n$-body problem variational methods periodic solutions convex optimization.

Author Details

Kuo-Chang Chen

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    Regular and Chaotic Dynamics, Vol. 28 (2023), Iss. 4-5 P.561

    https://doi.org/10.1134/S1560354723040044 [Citations: 0]