  In this paper, we show how the study of kinematics of a family of
trajectories of a classical mechanical system may be unified within the
framework of analysis of geodesic flows in Riemannian geometry and Relativity.
After setting up the general formalism, we explore it through studies on
various one and two dimensional systems. Quantities like expansion, shear and
rotation (ESR), which are more familiar to the relativist, now re-appear while
studying such families of trajectories in configuration space, in very simple
mechanical systems. The convergence/divergence of a family of trajectories
during the course of time evolution, the shear and twist of the area enclosing
the family, and the focusing/defocusing of the trajectories within a finite
time are investigated analytically for these systems. The understanding of the
configuration space developed through such investigations is elaborated upon,
and possible future avenues are pointed out.
