On the Simulation of Discontinuous Functions

Abstract

Discontinuous function constraints arise during the calculation of surface contact, stiction, and friction effects in studies of the behavior of complex systems. These nonlinear effects are mathematically defined by inequality constraints of the form 0≥g(x(t),t). The unknown in the problem is the time, t*, when the equality condition is reached. This paper presents an exact solution for t*, which is obtained by introducing a slack variable that replaces time as the independent variable, leading to an extended state-space that is noniteratively integrated to the constraint surface. Several applications are presented to demonstrate the method.