A Sharp Form of the Virial Theorem

In its classical form the Virial Theorem concerns the behavior of a system S of n mass particles acting under Newtonian attraction in such a fashion that the center of mass 0 remains fixed and the potential energy V satisfies V> — <*> for all positive time t. The latter condition, which is not always stated explicitly, guarantees the analyticity of the coordinates of the particles in the independent variable t\ in particular, it excludes collisions [2, pp. 324 ff.]. Let T denote the kinetic energy and h the (constant) total energy T+V. Let f denote the time average