Jump to ContentJump to Main Navigation
Analytical Mechanics for Relativity and Quantum Mechanics$
Users without a subscription are not able to see the full content.

Oliver Johns

Print publication date: 2005

Print ISBN-13: 9780198567264

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567264.001.0001

Show Summary Details
Page of

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: 24 January 2022

Lagrangian Mechanics with Time as a Coordinate

Lagrangian Mechanics with Time as a Coordinate

(p.267) 11 Lagrangian Mechanics with Time as a Coordinate
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Johns

Oxford University Press

In traditional analytical mechanics, it is assumed that the system traces out a path (one-dimensional curved line) in a D dimensional configuration space that is defined by writing each of the generalised coordinates as a function of the absolute, Newtonian time. The extended Lagrangian theory combines the traditional Lagrange equations and generalised energy theorem into a single set of equations, and restores the symmetry of the mathematical system. The traditional Lagrangian methods are analogous to the ‘coordinate parametric method’ in the calculus of variations and to the recommended ‘general parametric method’ presented earlier. This chapter discusses Lagrangian mechanics in which time is treated as a coordinate, extended momenta, invariance under change of parameter, change of generalised coordinates, redundancy of the extended Lagrange equations, forces of constraint, and reduced Lagrangians with time as a coordinate.

Keywords:   Lagrangian theory, Lagrange equations, time, generalised coordinates, extended momenta, invariance, constraint, Lagrangian mechanics

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .