Book contents
- Frontmatter
- Contents
- List of Symbols
- Preface
- Chapter 1 Introduction to Analysis of Low Speed Impact
- Chapter 2 Rigid Body Theory for Collinear Impact
- Chapter 3 Rigid Body Theory for Planar or 2D Collisions
- Chapter 4 3D Impact of Rough Rigid Bodies
- Chapter 5 Rigid Body Impact with Discrete Modeling of Compliance for the Contact Region
- Chapter 6 Continuum Modeling of Local Deformation Near the Contact Area
- Chapter 7 Axial Impact on Slender Deformable Bodies
- Chapter 8 Impact on Assemblies of Rigid Elements
- Chapter 9 Collision against Flexible Structures
- Chapter 10 Propagating Transformations of State in Self-Organizing Systems
- Appendix A Role of Impact in the Development of Mechanics During the Seventeenth and Eighteenth Centuries
- Appendix B Glossary of Terms
- Answers to Some Problems
- References
- Index
Chapter 10 - Propagating Transformations of State in Self-Organizing Systems
Published online by Cambridge University Press: 08 January 2010
- Frontmatter
- Contents
- List of Symbols
- Preface
- Chapter 1 Introduction to Analysis of Low Speed Impact
- Chapter 2 Rigid Body Theory for Collinear Impact
- Chapter 3 Rigid Body Theory for Planar or 2D Collisions
- Chapter 4 3D Impact of Rough Rigid Bodies
- Chapter 5 Rigid Body Impact with Discrete Modeling of Compliance for the Contact Region
- Chapter 6 Continuum Modeling of Local Deformation Near the Contact Area
- Chapter 7 Axial Impact on Slender Deformable Bodies
- Chapter 8 Impact on Assemblies of Rigid Elements
- Chapter 9 Collision against Flexible Structures
- Chapter 10 Propagating Transformations of State in Self-Organizing Systems
- Appendix A Role of Impact in the Development of Mechanics During the Seventeenth and Eighteenth Centuries
- Appendix B Glossary of Terms
- Answers to Some Problems
- References
- Index
Summary
Molecules far from equilibrium have far reaching sensitivity whereas those near equilibrium are sensitive to local effects only,
Ilya Prigogine, Cambridge Lecture, 1995A ball that falls in a gravitational field before colliding against a flat surface will rebound from the surface with a loss of energy that depends on the coefficient of restitution. If the ball is free, it will continue bouncing on the surface in a series of collisions; these arise because in each collision the ball is partly elastic and during the period between collisions the ball is attracted towards the surface by gravity. In Chapter 2 it was shown that an inelastic ball (0 < e* < 1) which is bouncing on a level surface in a gravitational field has both a period of time between collisions and a bounce height that asymptotically approach zero as the number of collisions increases. In other words, with increasing time this dissipative system asymptotically approaches a stable attractor – the equilibrium configuration where the ball is resting on the level surface.
Some other systems can experience energy input during each cycle of impact and flight; consequently these systems exhibit more complex behavior. For example, a pencil has a regular hexagonal cross-section with six vertices. If the pencil rolls down a plane, the mean translational speed of the axis asymptotically approaches a steady mean speed of rolling where the kinetic energy dissipated by the collision of a vertex against the plane equals the loss in gravitational potential energy as the pencil rolls from one flat side to the next.
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- Impact Mechanics , pp. 219 - 247Publisher: Cambridge University PressPrint publication year: 2000