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Chapter 2 - Rigid Body Theory for Collinear Impact

Published online by Cambridge University Press:  08 January 2010

W. J. Stronge
Affiliation:
University of Cambridge
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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.

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Chapter
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Impact Mechanics , pp. 21 - 34
Publisher: Cambridge University Press
Print publication year: 2000

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