Explain the concept of complementarity constraints, both for scalar and vector variables.
Formulate a linear complementarity problem (LCP).
Give a general prescription for a linear complementarity system (LCS, aka linear dynamical complementarity problem, LDCP).
Explain the essence of time-stepping numerical methods for simulating dynamical systems with complementarity constraints. In particular, show how the complementarity constraints are combined with an implicit or semi-explicit Euler scheme.
Skills (use the knowledge to solve a problem)
Formulate a (model of a) given mechanical system with unilateral constraints (hard stops) as a linear complementarity system.
Write a computer code (in Matlab, Julia, …) that implements a simple time-stepping numerical scheme for a simulation of a simple mechanical system with complementarity constraints (hard stops, dry friction).