The orbits (unparametrized solutions) of a mechanical system q'' = f(q), where q is a point in an affine space, can be described in a 'projective' way viewing this affine space as homogeneous coordinates as has been developed in the works of Albouy. On the other hand, Kasner has given a number of curious geometric properties characterizing orbits of such mechanical systems, and in this talk we will examine some relations of these geometric properties to the structure of projective dynamics, as well as some analogous geometric properties for various types of projections of n-body systems.
Alain Albouy, Alain Chenciner, Jacques Laskar
