We demonstrate that the formalism for the calculation of Jacobi’s 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 [Proceedings of the Benares Mathematical Society 2, 53 (1940)] dating from almost 70 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.
Jacobi's last multiplier and Lagrangians for multidimensional linear systems / NUCCI, Maria Clara; P. G. L. LEACH. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 49:7(2008), pp. 073517-1-073517-8. [10.1063/1.2956486]
Jacobi's last multiplier and Lagrangians for multidimensional linear systems
NUCCI, Maria Clara;
2008
Abstract
We demonstrate that the formalism for the calculation of Jacobi’s 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 [Proceedings of the Benares Mathematical Society 2, 53 (1940)] dating from almost 70 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
