On geodesic lines and first integrals in the configuration subspace V(m)/spl sub/V(n) evaluated from the problem of time minimization in case of displacement of a dynamical system in a configuration space V(n)

The purpose of this paper is to show that in the case of a conservative dynamical system subject to the action of holonomic scleronomic constraints, generalized forces (controls) are of the same form as in the case of motion of a dynamical system on Painleve´s singular trajectories which represent geodesic lines. We show that, for a whole range of problems trajectories of a dynamical system in a subspace V(m) included in the configuration space V(n) (m/spl les/n) represent, in fact, geodesic lines. Results are illustrated by example.