| Description |
1 online resource (xii, 268 pages) : illustrations (some color) |
| Series |
Springer series in solid and structural mechanics, 2195-3511 ; volume 6 |
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Springer series in solid and structural mechanics ; v. 6. 2195-3511
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| Contents |
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 |
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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 |
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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 |
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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 |
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4.8.2 The Mass Moment of Inertia Is Finite: I<inftyReferences; 5 Collisions of Rigid Solids: Three Balls in a Box; 5.1 Introduction; 5.2 Three Balls Evolving on a Plane; 5.2.1 Numerical Examples; 5.3 Three Balls Evolving in a Box; 5.3.1 Numerical Examples; References; 6 Pedestrian Trajectories and Collisions in Crowd Motion; 6.1 Definitions -- 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 |
| Summary |
This book investigates collisions occurring in the motion of solids, in the motion of fluids but also in the motion of pedestrians in crowds. The duration of these presented collisions is short compared to the whole duration of the motion: they are assumed instantaneous. The innovative concept demonstrated in this book is that a system made of two solids, is deformable because their relative position changes. The definition of the velocities of deformation of the system introduced in the classical developments of mechanics, the principle of the virtual work and the laws of thermodynamics, allows a large range of applications such as crowd motions, debris flow motions, and shape memory alloys motions. The set of the applications is even larger: social sciences and mechanics are unified to predict the motion of crowds with application to transport management and to evacuation of theaters management |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed August 3, 2016) |
| Subject |
Collisions (Physics)
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SCIENCE -- Energy.
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SCIENCE -- Mechanics -- General.
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SCIENCE -- Physics -- General.
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Collisions (Physics)
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| Form |
Electronic book
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| ISBN |
9783662526965 |
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3662526964 |
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