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Advanced MechanicsFrom Euler's Determinism to Arnold's Chaos$
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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

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The restricted three body problem

The restricted three body problem

Chapter:
(p.95) 12 The restricted three body problem
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0012

This chapter includes a detailed study of the three body problem where one of the bodies is infinitesimal and the other two are in circular motion. This applies to the Sun-Jupiter-Asteroid, Earth-Moon-Satellite systems. Lagrange's surprising discovery of stable equilibrium points and orbits around them is explained. Jacobi's integral and Hill's regions are derived. A spin-off is a theory of stability in the presence of velocity dependent (Coriolis) forces: sometimes a maximum of the potential can be a stable equilibrium.

Keywords:   three body problem, Jacobi's integral, Coriolis forces, Hill's regions, stability

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