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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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Conservation laws

Conservation laws

Chapter:
(p.7) 2 Conservation laws
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0002

Every variable (function) on the phase space has a conjugate variable. If the action is independent of a variable, then its conjugate is a conserved quantity. Energy (Hamiltonian) is shown to be conserved. A digression applies this method to solve the problem for a minimal surface of revolution (catenary).

Keywords:   conservation laws, Hamiltonian, conjugate variable, catenary, phase space

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