Un problème hyperbolique du 2ème ordre avec contrainte unilatérale: La corde vibrante avec obstacle ponctuel

Abstract We consider the small transverse vibrations of a string that is constrained to stay on one side of a moving peg (clou in french). We give an appropriate modelization. Existence and uniqueness for the Cauchy Problem are proved. Conservation of energy is a consequence of the set of inequations which describe the model. Continuous dependence on initial data, convergence of penalization are proved and a variational formulation is given. A number of generalizations are presented. A continuous obstacle cannot be approximated by a point obstacle made out of a large number of pegs.