Mathematical Description of Unilateral Constraints for Discrete Mechanical Systems

The paper deals with mathematical description of unilateral constraints imposed on displacements and velocities. Discrete mechanical system are analyzed. Mathematical description of the problem concerning the interaction between material points and unilateral constraints is presented. Unilateral constraints can be defined as a model of a phenomenon occurring during the process of interaction between a material body and a displacement restriction. It was assumed that the reaction forces characterizing this interaction are elastic and the body deformation is small comparing with its displacements. Mathematical description of constraints is composed of geometrical conditions imposed on the body motion as well as a relationship between the reaction force and the body configuration. In this paper, geometrical characteristics of constraints are described using multi-valued mappings. The study focuses attention on the formulation of the problem with the use of the concept of unilateral constraints described by variational inequalities.