Direct integration of generalized Lie or dynamical symmetries of three degrees of freedom nonlinear Hamiltonian systems: integrability and separability

Lakshmanan, M. ; Senthil Velan, M. (1992) Direct integration of generalized Lie or dynamical symmetries of three degrees of freedom nonlinear Hamiltonian systems: integrability and separability Journal of Mathematical Physics, 33 (12). pp. 4068-4077. ISSN 0022-2488

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Official URL: http://link.aip.org/link/?JMAPAQ/33/4068/1

Related URL: http://dx.doi.org/10.1063/1.529858

Abstract

It is shown that by directly integrating the characteristic equation of the infinitesimals of the generalized Lie or dynamical symmetries associated with three degrees of freedom Hamiltonians, one can almost, by inspection, obtain the required involutive integrals of motion, whenever they exist. The method is illustrated for the coupled quartic and cubic oscillators considered earlier. Further, all the separable coordinates can be obtained by integrating a subset of the characteristic equation associated with the coordinate variables alone.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
Keywords:Integrable Systems; Lie Groups; Dynamical Groups; Symmetry Groups; Degrees of Freedom; Hamiltonian Function; Oscillators; Coordinates; Hamilton-jacobi Equations
ID Code:19534
Deposited On:22 Nov 2010 12:26
Last Modified:08 Jun 2011 07:16

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