Sliding and Crossing Dynamics in Extended Filippov Systems

In spatial contact problems of rigid bodies, Coulomb friction results in dynamical systems with codimension-2 discontinuity manifolds, which are outside the scope of piecewise smooth dynamical systems. This motivated the authors to extend Filippov systems to codimension-2 discontinuity manifolds, which leads to the definition of extended Filippov systems. In these systems, sliding and crossing regions can be defined analogously to those of standard Filippov systems. A convex construction of the sliding vector is also presented in the paper. The developed methods are demonstrated on mechanical problems with spatial Coulomb friction.