Lagrangians Galore

Details Lagrangians Galore Lagrangians Galore

2007-06-07

arxiv.org/abs/0706.1008v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages

Scientific paper

10.1063/1.2821612

Searching for a Lagrangian may seem either a trivial endeavour or an impossible task. In this paper we show that the Jacobi last multiplier associated with the Lie symmetries admitted by simple models of classical mechanics produces (too?) many Lagrangians in a simple way. We exemplify the method by such a classic as the simple harmonic oscillator, the harmonic oscillator in disguise [H Goldstein, {\it Classical Mechanics}, 2nd edition (Addison-Wesley, Reading, 1980)] and the damped harmonic oscillator. This is the first paper in a series dedicated to this subject.

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