Collisions engineering : theory and applications / Michel Frémond.

Preface; Contents; 1 Introduction; 2 The Theory: Mechanics. An Example: Collision of a Point and a Plane; 2.1 A System Made of a Point and a Plane; 2.2 The Velocities; 2.3 The Velocity of Deformation; 2.4 The Principle of Virtual Work; 2.4.1 The Work of the Acceleration Forces; 2.4.2 The Work of the External Forces; 2.4.3 The Work of the Internal Forces; 2.5 The Equations of Motion; 2.5.1 Properties of the Equations of Motion; 2.6 The Laws of Thermodynamics; 2.6.1 The First Law; 2.6.2 The Second Law; 2.7 The Constitutive Laws; 2.7.1 The Free Energy and the Non Dissipative Forces

2.7.2 The Dissipative Forces2.8 Examples of Collisions with Internal Forces Defined #x83;; 2.8.1 First Example; 2.8.2 Second Example; 2.8.3 Third Example. Interpenetration Is Possible; 2.9 Examples of Dissipative Forces Defined with a Function of Dissipation; 2.9.1 The Coulomb's Friction Law; 2.9.2 The Coulomb's Collision Law; 2.9.3 Experimental Results; 2.9.4 Relationships Between Smooth Friction and Collision Constitutive Laws; References; 3 The Theory: Mechanics and Thermics. An Example: Collision of Two Balls; 3.1 Introduction; 3.2 The Velocities and the Velocities of Deformation

3.3 The Principle of Virtual Work and the Equations of Motion3.4 The Virtual Works; 3.4.1 The Theorem of Kinetic Energy; 3.5 The Equations of Motion; 3.6 Smooth Evolution of Two Balls with Thermal Effects; 3.6.1 Laws of Thermodynamics for a Ball; 3.6.2 Laws of Thermodynamics for the System; 3.6.3 The Constitutive Laws; 3.6.4 An Example; 3.7 Collisions of Two Balls with Thermal Effects; 3.7.1 First Law of Thermodynamics for a Ball; 3.7.2 Second Law of Thermodynamics for a Ball; 3.7.3 A Useful Inequality for a Ball; 3.7.4 The First Law for the System; 3.7.5 The Second Law for the System

3.7.6 A Useful Inequality for the System3.7.7 The Constitutive Laws; 3.7.8 An Example of Thermal Effects Due to Collisions; 3.8 Phase Change and Collisions; 3.9 Experimental Results; References; 4 Collisions of Rigid Solids: Three Disks in a Plane; 4.1 Introduction; 4.2 The Velocities; 4.3 The Velocities of Deformation; 4.4 The Work of the Interior Forces; 4.5 The Work of the Acceleration Forces; 4.6 The Equations of Motion; 4.7 The Constitutive Laws; 4.7.1 Solution of the Equations; 4.8 Numerical Examples; 4.8.1 The Mass Moment of Inertia Is Infinite: I=infty

4.8.2 The Mass Moment of Inertia Is Finite: I Phenomena of Typical Crowd Self-Organization; 6.2 The Current Methods for Modeling Crowd Movement; 6.2.1 Macroscopic Models; 6.2.2 Microscopic Models; 6.3 The Proposed 2D Discrete Model; 6.4 Multiple Contacts' Detection