Application of the field-momentum method to rheonomic dynamics

Abstract

The field-momentum method, recently introduced by the author, is applied to the study of motion and conservation laws of the rheonomic (i.e. time dependent) linear and non-linear dynamical systems with one degree of freedom. It is shown that the form of the Hamiltonian function of the dynamic systems (which is not a constant of motion for time-dependent system) can suggest the form of a class of quadratic conservation laws. It is demonstrated that the incomplete solutions of the field-momentum method can be combined with the Hamilton-Jacobi theory for finding the motion. © 1994.