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arXiv · 0709.3231

Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems

M. C. Nucci·P. G. L. Leach
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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.

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M. C. Nucci, P. G. L. Leach. 2007-09-20. Jacobi's Last Multiplier and Lagrangians for Multidimensional Systems. https://doi.org/10.1063/1.2956486

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