English

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

R2 v1 2026-06-21T09:19:31.905Z