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Advanced MechanicsFrom Euler's Determinism to Arnold's Chaos$
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Advanced Mechanics: From Euler's Determinism to Arnold's Chaos

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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 28 October 2021

The variational principle

The variational principle

Chapter:
(p.1) 1 The variational principle
Source:
Advanced Mechanics
Author(s):

S. G. Rajeev

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199670857.003.0001

This chapter looks at the equations of motion of a particle and describes the conditions that they present. It is not always a minimum, more commonly a saddle point. This chapter follows the ancient method of Euler and Lagrange to derive this fact. The quantum mechanical origin of this principle is also outlined: the average over all paths is dominated by the extremum in the limit of small Planck's constant.

Keywords:   Planck's constant, Lagrange, saddle point

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