Generalized Whittaker's equations for holonomic mechanical systems

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.