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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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Integrable systems

Integrable systems

Chapter:
(p.77) 10 Integrable systems
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0010

This chapter introduces action-angle variables and solves the general one dimensional conservative system. Bohr-Sommefeld quantization is shown to be the quantum analogue. Action angle variables for the radial Kepler problem are found to be generalized to the relativistic version. Action angle variables of the general integrable system are defined. The heavy top of Lagrange is solved as an example. The chapter includes an exercise to work out Kovalevskaya's surprising discovery of another solvable heavy top.

Keywords:   action-angle variables, Kepler problem, Lagrange, heavy top

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