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Unchained polygons and the N-body problem

Unchained polygons and the N-body problem We study both theoretically and numerically the Lyapunov families which bifurcate in the vertical direction from a horizontal relative equilibrium in ℝ3. As explained in [1], very symmetric relative equilibria thus give rise to some recently studied classes of periodic solutions. We discuss the possibility of continuing these families globally as action minimizers in a rotating frame where they become periodic solutions with particular symmetries. A first step is to give estimates on intervals of the frame rotation frequency over which the relative equilibrium is the sole absolute action minimizer: this is done by generalizing to an arbitrary relative equilibrium the method used in [2] by V. Batutello and S. Terracini. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Unchained polygons and the N-body problem

Regular and Chaotic Dynamics , Volume 14 (1) – Feb 10, 2009

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References (37)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354709010079
Publisher site
See Article on Publisher Site

Abstract

We study both theoretically and numerically the Lyapunov families which bifurcate in the vertical direction from a horizontal relative equilibrium in ℝ3. As explained in [1], very symmetric relative equilibria thus give rise to some recently studied classes of periodic solutions. We discuss the possibility of continuing these families globally as action minimizers in a rotating frame where they become periodic solutions with particular symmetries. A first step is to give estimates on intervals of the frame rotation frequency over which the relative equilibrium is the sole absolute action minimizer: this is done by generalizing to an arbitrary relative equilibrium the method used in [2] by V. Batutello and S. Terracini.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Feb 10, 2009

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