ASYMPTOTIC ANALYSIS OF DYNAMICAL-SYSTEMS SUBJECTED TO HIGH-FREQUENCY INTERACTIONS

A class of dynamic objects of general form subjected to rapidly changing, and, in particular, high frequency quasiperiodic external interactions is investigated. Conditions under which the system of equations of motion can be reduced to standard form are obtained. A transformation which allows an asymptotic analysis to be made using methods of separation of motion (the averaging method) which generalizes existing transformations is realized. In the first approximation the corresponding system is obtained and the autonomous system for slow displacements is studied qualitatively. The approach is illustrated by solving a number of problems for a system with one degree of freedom and variable parameters. Systems such as a non-linear oscillator and a simple pendulum are considered. External torques, kinematic excitation by vibrations of the point of suspension and parametric excitation by changing the length of the pendulum are taken as the high-frequency periodic interactions. Other models are considered.