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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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Hamiltonian mechanics

Hamiltonian mechanics

Chapter:
(p.83) 9 Hamiltonian mechanics
Source:
Relativity in Modern Physics
Author(s):

Nathalie Deruelle

Jean-Philippe Uzan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198786399.003.0009

This chapter gives a brief overview of Hamiltonian mechanics. The complexity of the Newtonian equations of motion for N interacting bodies led to the development in the late 18th and early 19th centuries of a formalism that reduces these equations to first-order differential equations. This formalism is known as Hamiltonian mechanics. This chapter shows how, given a Lagrangian and having constructed the corresponding Hamiltonian, Hamilton’s equations amount to simply a rewriting of the Euler–Lagrange equations. The feature that makes the Hamiltonian formulation superior is that the dimension of the phase space is double that of the configuration space, so that in addition to point transformations, it is possible to perform more general transformations in order to simplify solving the equations of motion.

Keywords:   Hamiltonian mechanics, Hamiltonian, Lagrangian, Euler–Lagrange equations, Newtonian equations of motion, first-order differential equations

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