Scalar force potentials in rigid multibody systems

These lectures treat the motion of finite-dimensional mechanical systems under the influence of set-valued force laws that are derived from scalar potential functions by generalized differentiation. Directional Newton-Euler equations in the configuration space are used to describe the impact-free non-smooth motion of the system. All forces are assumed to emanate from scalar force potentials on the displacement level and on the velocity level. No difference is made between constraint forces, impressed forces, and forces of intermediate type, as far as their representation via generalized gradients is concerned. This yields a clear mechanical interpretation of Lagrange multipliers as the scalar values of interaction forces acting in certain generalized directions and bridges the gap between the mathematical formulation of constraint forces and impressed forces. Some useful representations of the force laws are gathered by applying notation from convex analysis that provides a convenient handling of the decomposition of force laws on the one side and the introduction of variational calculus on the other side. Extensions of the classical variational principles in mechanics are discussed in this context. 70 Ch. Glocker 1