On the "universal" N=2 supersymmetry of classical mechanics

In this paper we continue the study of the geometrical features of a functi onal approach to classical mechanics proposed some time ago. In particular, we try to shed some light on a N = 2 "universal" supersymmetry which seems to have an interesting interplay with the concept of ergodicity of the sys tem. To study the geometry better we make this susy local and clarify pedag ogically several issues present in the literature. Secondly, in order to pr epare the ground for a better understanding of its relation to ergodicity, we study the system on constant energy surfaces. We find that the procedure of constraining the system on these surfaces injects in it some local Gras smannian invariances and reduces the N = 2 global susy to an N = 1.