Set-Valued Force Laws: Dynamics of Non-Smooth Systems

摘要: 1. Introduction.- 1.1 Friction Laws.- 1.2 Literature Survey.- 1.3 Subjects and Contents.- 2. Fundamental Concepts.- 2.1 Internal External Forces.- 2.2 The Law of Interaction.- 2.3 Dynamic Equilibrium.- 2.4 Virtual Work a System.- 2.5 Resultant Force Inertia Terms.- 3. Rigid Body Systems.- 3.1 Preliminaries on the Vector Product.- 3.2 Kinematics.- 3.3 Kinetics.- 3.4 Equilibrium Body.- 3.5 3.6 Classical Bilateral Constraints.- 3.7 Generalized Coordinates.- 4. Motion Discontinuity Events.- 4.1 Integration Functions.- 4.2 Displacements, Velocities, Accelerations.- 4.3 Restriction to Finite Numbers Discontinuities.- 5. Displacement Velocity Potentials.- 5.1 Directional Newton-Euler Equations.- 5.2 Set-Valued 5.3 Scalar Potential 5.4 On Modeling 6. Representation 6.1 Decomposition into Unilateral Primitives.- 6.2 Variational Formulations Upper Subderivatives.- 6.3 Convex Case: Conjugate Potentials Duality.- 6.4 Elements in Engineering Dynamics.- 7. Laws Different Kinematic Levels.- 7.1 Continuity Properties Trajectories.- 7.2 Acceleration Level.- 7.3 8. Index Sets LCP-Formulation.- 8.1 Sets.- 8.2 Formulation 8.3 Linear Complementarity Problem.- 8.4 Dual Principle Least 9. Principles 9.1 9.2 Gauss.- 9.3 Jourdain.- 9.4 d'Alembert/Lagrange.- 9.5 Remarks d'Alembert/Lagrange's Principle.- 10. Spatial Coulomb Friction.- 10.1 Geometry Surfaces.- 10.2 Contact 10.3 10.4 10.5 Sliding Contacts.- 10.6 Pyramid for Rolling 10.7 Cones NCP Formulations.- 10.8 A Differentiable 10.9 Example Remarks.- 11. Jumps due C0-Constraints.- 11.1 Impacts Mechanical 11.2 Model 11.3 Bilaterally Constrained Motion.- 11.4 Jump by Time-Scaling.- 11.5 Reflection.- 11.6 Reflections Collisions - 12. Electropneumatic Drilling Machine.- 12.1 Model.- 12.2 Simulations.- 13. Percussion 13.1 13.2 Mathematical Non-Contact.- 13.3 13.4 State Transitions.- 13.5 Results.- 14. Turbine Blade Damper.- 14.1 Damper Non-Contact Case.- 14.2 Kinematics Damping Device.- 14.3 Numerical 15. Concluding References.