Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems
Exactly Solvable and Integrable Systems
2009-11-13 v1
Abstract
We demonstrate that the formalism for the calculation of the Jacobi last multiplier for a one-degree-of-freedom system extends naturally to systems of more than one degree of freedom thereby extending results of Whittaker dating from more than a century ago and Rao ({\it Proc Ben Math Soc} {\bf 2} (1940) 53-59) dating from almost seventy years ago. We illustrate the theory with an application taken from the theory of coupled oscillators. We indicate how many Lagrangians can be obtained for such a system.
Cite
@article{arxiv.0709.3231,
title = {Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems},
author = {M. C. Nucci and P. G. L. Leach},
journal= {arXiv preprint arXiv:0709.3231},
year = {2009}
}
Comments
11 pages