Nonsmooth Mechanics : Models, Dynamics and Control (Hardcover, 2nd ed. 1999)

1 Distributional model of impacts.- 1.1 External percussions.- 1.2 Measure differential equations.- 1.2.1 Some properties.- 1.2.2 Additional comments.- 1.3 Systems subject to unilateral constraints.- 1.3.1 General considerations.- 1.3.2 Flows with collisions.- 1.3.3 A system theoretical geometric approach.- 1.3.4 Descriptor variable systems.- 1.4 Changes of coordinates in MDEs.- 1.4.1 From measure to Caratheodory systems.- 1.4.2 Decoupling of the impulsive effects (commutativity conditions).- 1.4.3 From measure to Filippov's differential equations: the Zhuravlev-Ivanov method.- 2 Approximating problems.- 2.1 Simple examples.- 2.1.1 From elastic to hard impact.- 2.1.2 From damped to plastic impact.- 2.1.3 The general case.- 2.2 The method of penalizing functions.- 2.2.1 The elastic rebound case.- 2.2.2 A more general case.- 2.2.3 Uniqueness of solutions.- 3 Variational principles.- 3.1 Virtual displacements principle.- 3.2 Gauss' principle.- 3.2.1 Additional comments and studies.- 3.3 Lagrange's equations.- 3.4 External impulsive forces.- 3.4.1 Example: flexible joint manipulators.- 3.5 Hamilton's principle and unilateral constraints.- 3.5.1 Introduction.- 3.5.2 Modified set of curves.- 3.5.3 Modified Lagrangian function.- 3.5.4 Additional comments and studies.- 4 Two bodies colliding.- 4.1 Dynamical equations of two rigid bodies colliding.- 4.1.1 General considerations.- 4.1.2 Relationships between real-world and generalized normal di-rections.- 4.1.3 Dynamical equations at collision times.- 4.1.4 The percussion center.- 4.2 Percussion laws.- 4.2.1 Oblique percussions with friction between two bodies.- 4.2.2 Rigid body formulation: Brach's method.- 4.2.3 Additional comments and studies.- 4.2.4 Rigid body formulation: Fremond's approach.- 4.2.5 Dynamical equations during the collision process: Darboux-Keller's shock equations.- 4.2.6 Stronge's energetical coefficient.- 4.2.7 3 dimensional shocks- Ivanov's energetical coefficient.- 4.2.8 A third energetical coefficient.- 4.2.9 Additional comments and studies.- 4.2.10 Multiple micro-collisions phenomenon: towards a global coef-ficient.- 4.2.11 Conclusion.- 4.2.12 The Thomson and Tait formula.- 4.2.13 Graphical analysis of shock dynamics.- 4.2.14 Impacts in flexible structures.- 5 Multiconstraint nonsmooth dynamics.- 5.1 Introduction. Delassus' problem.- 5.2 Multiple impacts: the striking balls examples.- 5.3 Moreau's sweeping process.- 5.3.1 General formulation.- 5.3.2 Application to mechanical systems.- 5.3.3 Existential results.- 5.3.4 Shocks with friction.- 5.4 Complementarity formulations.- 5.4.1 General introduction to LCPs and Signorini's conditions.- 5.4.2 Linear Complementarity Problems.- 5.4.3 Relationships with quadratic problems.- 5.4.4 Linear complementarity systems.- 5.4.5 Additional comments and studies.- 5.5 The Painleve's example.- 5.5.1 Lecornu's frictional catastrophes.- 5.5.2 Conclusions.- 5.5.3 Additional comments and bibliography.- 5.6 Numerical analysis.- 5.6.1 General comments.- 5.6.2 Integration of penalized problems.- 5.6.3 Specific numerical algorithms.- 6 Generalized impacts.- 6.1 The frictionless case.- 6.1.1 About "complete" Newton's rules.- 6.2 The use of the kinetic metric.- 6.2.1 The kinetic energy loss at impact.- 6.3 Simple generalized impacts.- 6.3.1 2-dimensional lamina striking a plane.- 6.3.2 Shock of a particle against a pendulum.- 6.4 Multiple generalized impacts.- 6.4.1 The rocking block problem.- 6.5 General restitution rules for multiple impacts.- 6.5.1 Introduction.- 6.5.2 The rocking block example continued.- 6.5.3 Additional comments and studies.- 6.5.4 3-balls example continued.- 6.5.5 2-balls.- 6.5.6 Additional comments and studies.- 6.5.7 Summary of the main ideas.- 6.5.8 Collisions near singularities: additional comments.- 6.6 Constraints with Amontons-Coulomb friction.- 6.6.1 Lamina with friction.- 6.7 Additional comments and studies.- 7 Stability of nonsmooth dynamical systems.- 7.1 General stability concepts.- 7.1.1 Stabili