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 2 - Rigid Body Theory for Collinear Impact
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
The value of a formalism lies not only in the range of problems to which it can be successfully applied but equally in the degree to which it encourages physical intuition in guessing the solution of intractable problems.
Sir Alfred Pippard, Physics Bulletin 20, 455, 1969.Two bodies, labeled B and B′, collide when they come together with an initial difference in velocity. Ordinarily they first touch at a point that will be termed the contact point C. During a very brief period of contact, the point C on the surface of body B is coincident with point C′ on the surface of body B′. If at least one of the bodies, B or B′, has a surface that is topologically smooth at the contact point (i.e., the surface has continuous curvature), there is a plane tangent to this surface at C; the coincident contact points C and C′ lie in this tangent plane. If both bodies are convex and the surfaces have continuous curvature near the contact point, then this tangent plane is tangential to both surfaces that touch at C; i.e., the surfaces of the colliding bodies have a common tangent plane. The direction of the normal to the tangent plane is specified by a unit vector n; this direction is termed the common normal direction. The contact force and changes in relative velocity at the contact point C will be resolved into components normal and tangential to the common tangent plane.
- Type
- Chapter
- Information
- Impact Mechanics , pp. 21 - 34Publisher: Cambridge University PressPrint publication year: 2000
- 3
- Cited by