Stability and convergence of mechanical systems with unilateral constraints

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Stability of motion is a key theme in mechanical system dynamics. This monograph systematically explores mechanical systems with unilateral constraints, such as contact, impact, and friction, which lead to non-smooth dynamical models. It begins with a discussion of the mathematical foundations of non-smooth analysis, measure and integration theory, and an introduction to non-smooth dynamical systems. Unilateral constraints are modeled using set-valued force laws from non-smooth mechanics, resulting in dynamical models that exhibit impulsive phenomena. The framework of measure differential inclusions is employed to formalize these models. The text presents stability results for these inclusions, which are then applied to nonlinear mechanical systems with unilateral constraints. The study concludes with an examination of convergence properties for a specific class of measure differential inclusions, highlighting a stability property relevant to systems with time-varying inputs, essential for controlling mechanical systems with unilateral constraints. This work not only offers a comprehensive stability theory for such mechanical systems but also serves as a tutorial on their modeling within the measure differential inclusions framework, appealing to engineers, scientists, and students in non-smooth mechanics and dynamics.