Numerical Analysis of Sliding Dynamics in Three-Dimensional Filippov Systems using SPT Method

Ivan Arango, John Taborda
We present the numerical analysis of sliding dynamics on the discontinuity boundary (DB) of three-dimensional (3D) Filippov systems using an integration-free method denominated Singular Point Tracking (SPT). Many physical applications in engineering can be modelled as Filippov systems. Sliding dynamics due to non-smooth phenomena such as friction, hysteresis or switching are inherent to Filippov systems. The analysis of sliding dynamics have many mathematical and numerical difficulties. Several
more » ... well-known numerical problems can be avoid using integration-free methods. Three-dimensional Filippov systems are being studied extensively because these systems still have many open problems. In this paper, we present a first attempt to extend the SPT method to 3D Filippov systems. The discontinuity boundary (DB) is characterized using geometric criterions based on angular evaluations. Eighteen basic points on DB are distinguished and eight basic scenarios on DB are defined. Finally, local and global bifurcation scenarios are conceptualized with the SPT method and some illustrative examples are given.