ON THE DEFINITION OF A FAMILY OF SETS OF CANONICAL ELEMENTS FOR HYPERBOLIC MOTION

The transition from a canonical set of Delaunay-like elements to anoth er one of the DS type, both kinds of sets being applicable to point ma sses moving along hyperbolic trajectories in problems of orbital motio n, is performed by means of a completely canonical transformation deri ved from a generating function. The two-body Hamiltonian is simplified after the introduction of a fictitious time as the new independent va riable; in particular, the arbitrariness in this reparametrizing trans formation allows us to recover. as special cases, independent variable s analogous to the corresponding classical anomalies in elliptic motio n,