Dynamical systems with multiplicative random implse process excitation

摘要

Dynamical systems with multiplicative (parametric) random impulse process excitation are considered. A technique is developed to convert the usual differential equation of motion (physical equation) into an Ito's type stochastic differential equation for random impulse process excitation multiplicative to the velocity term of the equation of motion. The use is made of the generalized Ito's differential rule and of the properties of the increments of the underlying regular random counting process. It is found that the diffusion term rather than the drift term has to be corrected. For linear and quadratic velocity terms the corrected diffusion terms are given in a closed form.