Lagrangians Galore
Exactly Solvable and Integrable Systems
2009-11-13 v1 Mathematical Physics
math.MP
Classical Physics
Abstract
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.
Keywords
Cite
@article{arxiv.0706.1008,
title = {Lagrangians Galore},
author = {M. C. Nucci and P. G. L. Leach},
journal= {arXiv preprint arXiv:0706.1008},
year = {2009}
}