STOCHASTIC MECHANICAL SYSTEMS WITH A NONRETAINING CONSTRAINT

Holonomic mechanical systems with a non-retaining constraint and absolutely elastic collisions with the constraints subject to normal ''white noise'' perturbation forces are considered. The motion is defined and the problem of analysing such systems is formulated. It is shown that the Fokker-Planck-Kolmogorov equation for the one-dimensional probability distribution density of the state vector of systems free from a non-retaining constraint also governs the one-dimensional distribution density for the systems under consideration. Steady regimes in the restricted sense are studied and an approximate method of analysing such systems is proposed. Examples are considered.