International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 2, Pages 245-253
doi:10.1155/S0161171278000289
Generalized Whittaker's equations for holonomic mechanical
systems
Department of Mathematics, Government College, Lahore, Pakistan
Received 23 June 1977
Copyright © 1978 Munawar Hussain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this paper the classical theorem “a conservative holonomic dynamic system is invariantly connected with a certain differential form” is generalized to group variables. This general theorem is then used to reduce the order of a Hamiltonian system by the use of the integral of energy. Equations of motion of the reduced system so obtained are derived which are the so-called generalized Whittaker's equations. Finally an example is given as an application of the theory.