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The zero angular momentum, three-body problem: All but one solution has syzygies

Published online by Cambridge University Press:  01 December 2007

RICHARD MONTGOMERY
RICHARD MONTGOMERY*
Affiliation:
Mathematics Department, UC Santa Cruz, Santa Cruz, CA, 95064, USA (email: [email protected])
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Abstract

A syzygy in the three-body problem is a collinear instant. We prove that, with the exception of Lagrange’s solution, every solution to the zero angular momentum, Newtonian three-body problem suffers syzygies. The proof works for all mass ratios.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1933 - 1946
Copyright
Copyright © Cambridge University Press 2007

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