Chapter

The three body problem

S. G. Rajeev

in Advanced Mechanics

Published in print July 2013 | ISBN: 9780199670857
Published online December 2013 | e-ISBN: 9780191775154 | DOI: https://dx.doi.org/10.1093/acprof:oso/9780199670857.003.0011
The three body problem

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This chapter derives the consequences of scale invariance in the three body problem. Jacobi co-ordinates are introduced. The orbits are geodesics in a certain metric. The three body problem with inverse cube force is shown to be more symmetric. Montgomery's ‘pair of pants’ metric is derived. The orbits are geodesics in a metric of negative curvature on the plane with three points removed. The Virial Theorem is suggested as an exercise.

Keywords: three body problem; Jacobi co-ordinates; negative curvature; geodesics

Chapter.  3006 words. 

Subjects: Atomic, Molecular, and Optical Physics

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