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Volume 37, Issue 1
Keplerian Action, Convexity Optimization, and the 4-Body Problem

Kuo-Chang Chen

DOI: 10.4208/ata.2021.pr80.04

Anal. Theory Appl., 37 (2021), pp. 24-58.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

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

  • AMS Subject Headings

70F10, 37J51

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-37-24, author = {Chen , Kuo-Chang}, title = {Keplerian Action, Convexity Optimization, and the 4-Body Problem}, journal = {Analysis in Theory and Applications}, year = {2021}, volume = {37}, number = {1}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2021.pr80.04}, url = {http://global-sci.org/intro/article_detail/ata/18763.html} }
TY - JOUR T1 - Keplerian Action, Convexity Optimization, and the 4-Body Problem AU - Chen , Kuo-Chang JO - Analysis in Theory and Applications VL - 1 SP - 24 EP - 58 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/ata.2021.pr80.04 UR - https://global-sci.org/intro/article_detail/ata/18763.html KW - $n$-body problem, variational methods, periodic solutions, convex optimization. AB -

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.

Chen , Kuo-Chang. (2021). Keplerian Action, Convexity Optimization, and the 4-Body Problem. Analysis in Theory and Applications. 37 (1). 24-58. doi:10.4208/ata.2021.pr80.04
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