PHYSICAL ASSESSMENT OF MECHANISMS OF INFLUENCE ON OBJECTS WITH MANY DEGREES OF FREEDOM

Abstract

The research develops a serial-parallel method for the time description of processes in inertial objects under the influence of basis functions. The author proposes a method for solving systems of first-order differential equations, which allows determining the time constants and amplitudes of the exponential functions of the Heaviside formula. The method provides the fundamental possibility of theoretical solutions to linear and nonlinear problems of analyzing processes in inertial objects with any number of storage devices. A physical model of an inertial object with m reactances is presented, which is described either by a differential equation of the m-th order, or by a system of m differential equations of the first order. When implementing this method, any action is decomposed into a unitary time functional series, each member of which is an elementary basis function with specified frequency-time parameters and an amplitude equal to the input action averaged over the active part of the period of the basis function. The resulting mathematical descriptions of the mechanisms of action are common to all problems of analyzing inertial systems and serve as the basis for solving applied problems, primarily for studying the beneficial and harmful effects of action.