International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 2, Pages 245-253

Generalized Whittaker's equations for holonomic mechanical systems

Munawar Hussain

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.


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.