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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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Introduction to Lagrangian Mechanics

Introduction to Lagrangian Mechanics

Chapter:
(p.24) 2 Introduction to Lagrangian Mechanics
Source:
Analytical Mechanics for Relativity and Quantum Mechanics
Author(s):

Oliver Davis Johns

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780191001628.003.0002

This chapter argues that modern analytical mechanics began with the work of the eighteenth-century mathematicians who elaborated Newton's ideas. Without changing Newton's fundamental principles, Euler, Laplace, and Lagrange developed elegant computational methods for the increasingly complex problems to which Newtonian mechanics was being applied. The Lagrangian formulation of mechanics is merely an abstract way of writing Newton's second law. When simple Cartesian coordinates are replaced by the most general variables capable of describing the system adequately, the Lagrange equations do not change. The vector methods fail when a mechanical system is described by systems of coordinates much more general than the standard curvilinear ones. The Lagrangian method frees one from the task of keeping track of the components of force vectors and the identities of the particles upon which they act.

Keywords:   modern analytical mechanics, Euler, Laplace, Lagrange, Lagrangian formulation, Cartesian coordinates

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