Jump to ContentJump to Main Navigation
Advanced MechanicsFrom Euler's Determinism to Arnold's Chaos$
Users without a subscription are not able to see the full content.

S. G. Rajeev

Print publication date: 2013

Print ISBN-13: 9780199670857

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199670857.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 25 May 2019

The three body problem

The three body problem

Chapter:
(p.87) 11 The three body problem
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0011

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .