Multibody dynamics started with the ideas of Jacob and Daniel Bernoul- li and later on with d'Alembert's principle. In establishing a solution for the problem of the center of oscillation for a two-mass-pendulum Jacob Ber- noulli spoke about balancing the profit-and-Ioss account with respect to the motion of the two masses. Daniel Bernoulli extended these ideas to a chain pendulum and called forces not contributing to the motion "lost forces," thus being already very close to d'Alembert's principle. D'Alembert considered a "system of bodies, which are interconnected in some arbitrary way. "...

This volume introduces basic concepts necessary for treatment of inequality problems in finite degree of freedom dynamics. The lectures cover a broad area of non-smooth dynamics from primal and dual energy functions in variational and differential form to various application problems.