Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems

Details Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems

2007-09-20

arxiv.org/abs/0709.3231v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages

Scientific paper

10.1063/1.2956486

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.

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