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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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Hamilton’s principle

Hamilton’s principle

Chapter:
(p.43) 7 Hamilton’s principle
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0007

The variational principle is formulated in first order form, deriving Hamilton's equations. Poisson brackets are found as generating infinitesimal canonical transformations. Symmetries are found to lead to conservation laws. A glimpse of the star product of quantum mechanics is given: the classical Poisson bracket is its infinitesimal approximation. In an exercise, the quantum harmonic oscillator is solved in the star product formalism.

Keywords:   Hamilton's equations, Poisson brackets, symmetries, star product

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