Modelling of dynamical systems with motion dependent discontinuities

The paper introduces two concepts for describing and solving dynamical syst ems with motion dependent discontinuities such as clearances, impacts, dry friction, or combination of these phenomena. The first approach assumes any dynamic system can be considered as continuous in a finite number of conti nuous subspaces, which together form so-called global hyperspace. Global so lution is obtained by "gluing" local solutions obtained by solving the prob lem in the continuous subspaces. An efficient numerical algorithm is presen ted, and then used to solve dynamics of a piecewise oscillator, which has b een also verified experimentally. The second approach considers that in rea lity the system parameters do not change in an abrupt manner. Therefore, a smooth contiunuous function is used to model a transition between the subsp aces, in particular the sigmoid function is employed. This allows to contro l the degree of abruptness on the intersections of the continuous subspaces . An asymmetrical, piecewise linear oscillator has been examined to provide recommendations regarding validity of this approach. (C) 2000 Elsevier Sci ence Ltd. All rights reserved.