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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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Lagrangian Mechanics with Time as a Coordinate

Lagrangian Mechanics with Time as a Coordinate

(p.290) (p.291) 13 Lagrangian Mechanics with Time as a Coordinate
Analytical Mechanics for Relativity and Quantum Mechanics

Oliver Davis Johns

Oxford University Press

This chapter presents an extended theory in which the traditional Lagrange equations and generalised energy theorem are combined into a single set of equations that restore the symmetry of the mathematical system. The traditional Lagrangian methods are analogous to the ‘coordinate parametric method’ in the calculus of variations, while the extended Lagrangian theory is analogous to the recommended ‘general parametric method’. The generalised energy theorem of traditional Lagrangian theory, which had been a separate equation analogous to the ‘second form’ of the Euler-Lagrange equations, gets restored to its proper place as just another of the extended Lagrange equations, which now form a complete set of equations appropriate to the problem.

Keywords:   traditional Lagrange equations, generalized energy theorem, mathematical system, coordinate parametric method, general parametric method

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