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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–Jacobi theory

Hamilton–Jacobi theory

(p.69) 9 Hamilton–Jacobi theory
Advanced Mechanics

S. G. Rajeev

Oxford University Press

This chapter derives the Hamilton-Jacobi equation. Euler's two centre problem is solved by using separation of variables in the elliptical co-ordinate system. The connection to the eikonal equation of optics as well as to the Schrödinger equation of quantum mechanics is explained.

Keywords:   Hamilton-Jacobi equation, eikonal equation, Schrödinger equation, Euler's two centre problem, separation of variables

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