Vibratory energy of a conservative mechanical system

Abstract

203 The motion of a conservative mechanical system with holonomic bonds with a finite number of degrees of freedom under the effect of vibrations, the fre� quency of which considerably exceeds the frequencies of selfinduced vibrations of the system, is considered. For the averaged motion, the effect of vibration leads to the appearance of an additional summand of the potential energy (vibratory energy). The term "vibra� tory energy" was presented in the wellknown mono� graph Mechanics by Landau and Lifshits (1), and its derivation was performed only for systems with one degree of freedom. In this work, for a system with an arbitrary number of degrees of freedom, the derivation of the dependence of the vibratory energy on the gen� eralized coordinates and vibratory law is presented and its difference from (1) is shown. The minimum of the effective potential energy corresponds to stable steadystate motion. An example of determination of stable steadystate motions of a spherical pendulum with the arbitrary threedimensional vibration of the suspension center is presented.