Mechanical systems with unilateral constraints: Controlled singularity approach

Admitting the introduction of the impulsive control actions during singular phases of the dynamical system motion, such as changes in dimension, and discontinuities in the state, a well-posed representation of the discontinuous limiting motion of mechanical systems with unilateral constraints in terms of differential equations with measure is developed. This representation is mapped into a detailed multi-scale system description via a space-time transformation. The resulting framework, which includes the equations of the detailed and limit dynamics connected via the space-time transformation, is used to describe a difficult to model class of systems - mechanical systems with impulsive control actions introduced by a collision-type system interaction with nonstationary controllable constraints.