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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

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

Oliver Johns

Oxford University Press

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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