Some dynamic systems have hard constraints that need to be modeled as inequalities. When the inequality becomes equality, some aspect of the system (and the differential equation) needs to change. Complementarity conditions are often used to describe such changes: in mechanical impact, the separation between bodies and the contact forces keeping them from penetrating are both non-negative, and if one is positive, the other must be zero. This approach to modeling dynamic systems with constraints can be applied to other systems (electrical circuits with ideal diodes, networks of queues, dynamic traffic flow).
Recent work on computation and simulation of dynamic systems is included, as well as older more fundamental work on existence and uniqueness of solutions.