Force structure effect on the stability of motion under integrally small perturbations

The stability of dynamical systems for various types of perturbations has been considered by many authors. The stability of motion of dynamical systems subject to integrally small perturbation forces active on a finite time interval is considered in [1–3]. It is assumed that the perturbation forces are specified in terms of functions of a fairly general class, namely, the class of distributions (in particular, functions of the pulse type). This paper is aimed at stability problems describing the motion (or a state of equilibrium) of mechanical systems with holonomic stationary constraints, in the case of integrally small perturbations in the presence of additional gyroscopic and dissipative forces. We give a definition of the stability with respect to integrally small perturbations and formulate the main results obtained in this connection. We establish sufficient conditions for the stability or instability of motion (or a state of equilibrium) of mechanical systems with holonomic stationary constraints in the case of integrally small perturbations.