Set-Valued Force Laws

Dynamics of Non-Smooth Systems

AvChristoph Glocker

Inbunden, Engelska, 2001

Del i serien Lecture Notes in Applied and Computational Mechanics

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Beskrivning

This is one out of a few books which treat the dynamics of non-smooth systems in finite degree of freedom mechanics. Based on the classical multibody system approach set-valued force laws are introduced to fully encompass situations like the frictional contact problem, unilateral constraints, the behavior of one-way clutches, and even velocity jumps not related to any kind of collisions. The book concentrates on modern mathematical methods and concepts from optimization theory combined with classical analytical mechanics, such that it should be valuable for people working on discontinuity problems in nearly all branches of classical physics.

Produktinformation

Utgivningsdatum:2001-05-22
Mått:155 x 235 x undefined mm
Format:Inbunden
Språk:Engelska
Serie:Lecture Notes in Applied and Computational Mechanics
Antal sidor:222
Förlag:Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN:9783540414360

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Innehållsförteckning

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