Jean Jacques Moreau's work explores the dynamics of mechanical systems with finite degrees of freedom, focusing on unilateral contact and dry friction. The paper introduces a framework using convex analysis and measure theory to handle non-smooth dynamics, where velocity is not necessarily differentiable but has bounded variation. The dynamics are governed by measure differential inclusions, which account for both smooth motions and velocity jumps. Unilateral constraints are described by inequalities, and the feasible region is defined by these constraints. The paper also addresses dry friction, using a generalized form of Coulomb's law, and discusses the implications of these formulations for numerical algorithms. Key concepts include the tangent cone, normal cone, and the use of convex analysis to handle non-smooth effects. The paper emphasizes the importance of considering both the geometric constraints and the associated constraint forces, and it provides a foundation for numerical methods that can handle discontinuities and non-smooth behaviors in mechanical systems. The work also discusses the challenges of modeling dry friction and the need for robust numerical techniques to simulate such systems accurately.Jean Jacques Moreau's work explores the dynamics of mechanical systems with finite degrees of freedom, focusing on unilateral contact and dry friction. The paper introduces a framework using convex analysis and measure theory to handle non-smooth dynamics, where velocity is not necessarily differentiable but has bounded variation. The dynamics are governed by measure differential inclusions, which account for both smooth motions and velocity jumps. Unilateral constraints are described by inequalities, and the feasible region is defined by these constraints. The paper also addresses dry friction, using a generalized form of Coulomb's law, and discusses the implications of these formulations for numerical algorithms. Key concepts include the tangent cone, normal cone, and the use of convex analysis to handle non-smooth effects. The paper emphasizes the importance of considering both the geometric constraints and the associated constraint forces, and it provides a foundation for numerical methods that can handle discontinuities and non-smooth behaviors in mechanical systems. The work also discusses the challenges of modeling dry friction and the need for robust numerical techniques to simulate such systems accurately.