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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2005

Print ISBN-13: 9780198567264

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567264.001.0001

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Hamilton’s Principle and Noether’s Theorem

Hamilton’s Principle and Noether’s Theorem

Chapter:
(p.305) 13 Hamilton’s Principle and Noether’s Theorem
Source:
Analytical Mechanics for Relativity and Quantum Mechanics
Author(s):

Oliver Johns

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567264.003.0013

This chapter presents extended forms of Hamilton’s principle and the phase space Hamilton’s principle based on the extended Lagrangian and Hamiltonian methods developed earlier. It also discusses Noether’s theorem, a method for using symmetries of the extended Lagrangian to identify quantities that are conserved during the motion of the system. Noether’s theorem is a powerful technique for discovering conserved quantities in complex Lagrangian systems. The basics of the method are analysed in the simple context of Lagrangian systems with a finite number of degrees of freedom.

Keywords:   Noether’s theorem, Hamilton’s principle, phase space, motion, Lagrangian systems, degrees of freedom, conserved quantities

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