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

A class of dynamic objects of general form subjected to rapidly changi ng, and, in particular, high frequency quasiperiodic external interact ions is investigated. Conditions under which the system of equations o f motion can be reduced to standard form are obtained. A transformatio n which allows an asymptotic analysis to be made using methods of sepa ration of motion (the averaging method) which generalizes existing tra nsformations is realized. In the first approximation the corresponding system is obtained and the autonomous system for slow displacements i s studied qualitatively. The approach is illustrated by solving a numb er of problems for a system with one degree of freedom and variable pa rameters. Systems such as a non-linear oscillator and a simple pendulu m 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 intera ctions. Other models are considered.