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Analytical Mechanics for Relativity and Quantum Mechanics$
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Oliver Johns

Print publication date: 2011

Print ISBN-13: 9780191001628

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780191001628.001.0001

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Hamilton's Principle

Hamilton's Principle

(p.119) 6 Hamilton's Principle
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Davis Johns

Oxford University Press

This chapter shows that the general calculus of variations can be used to derive variational principles in mechanics. Two different, but closely related, variational principles are presented here: Hamilton's Principle and the phase-space Hamilton's Principle. It is believed by some authors that variational principles are the foundations of physics. For example, the classic analytical mechanics text of Landau and Lifshitz (1976) writes an action function on page two, and derives the whole of mechanics from it, including Newton's laws. Whether this is a fair judgment or not, it is certainly true that variational principles play a crucial role in quantum theory, general relativity, and theoretical physics in general.

Keywords:   variational principles, Hamilton's Principle, foundations of physics, Landau, Lifshitz

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