  The evolution of a Lagrangian mechanical system is variational. Likewise,
when dealing with a hybrid Lagrangian system (a system with discontinuous
impacts), the impacts can also be described by variations. These variational
impacts are given by the so-called Weierstrass-Erdmann corner conditions.
Therefore, hybrid Lagrangian systems can be completely understood by
variational principles.
  Unlike typical (unconstrained / holonomic) Lagrangian systems,
nonholonomically constrained Lagrangian systems are not variational. However,
by using the Lagrange-d'Alembert principle, nonholonomic systems can be
described as projections of variational systems. This paper works out the
analogous version of the Weierstrass-Erdmann corner conditions for nonholonomic
systems and examines the billiard problem with a rolling disk.
