Two Interpretations of Rigidity in Rigid-Body Collisions

We distinguish between, and discuss the applicability of two levels of rigidity in rigid-body collision modeling. For rigidity in the strong force-response sense, collisional contact deformations must be highly localized. The bodies then move according to second-order rigid-body mechanics during the collision. Incremental collision laws and most collision models using continuum mechanics for the contact region depend on force-response rigidity. For rigidity in the weaker impulse-response sense, the deformations need not be localized but displacements during the collision need to be small everywhere. Only the time-integrated rigid-body equations, involving before-collision and after-collision velocities, then need apply. Although a force-response rigid body is also impulse-response rigid the converse is not true. Algebraic collision laws depend only on impulse-response rigidity. Elastic vibration models of collisions are also generally consistent with impulse-response rigidity.

[1]  Lord Rayleigh.  XXII. On the production of vibrations by forces of relatively long duration, with application to the theory of collisions , 1906 .

[2]  R. D. Mindlin.  Elastic Spheres in Contact Under Varying Oblique Forces , 1953 .

[3]  A. Ishlinsky.  On the dynamics of a system of rigid bodies , 1973 .

[4]  J. N. Fawcett,et al.  The Role of Elastic Tangential Compliance in Oblique Impact , 1981 .

[5]  Thomas R. Kane,et al.  THEORY AND APPLICATIONS , 1984 .

[6]  J. Keller.  Impact With Friction , 1986 .

[7]  Edmund Taylor Whittaker,et al.  A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: INDEX OF TERMS EMPLOYED , 1988 .

[8]  W. Stronge.  Rigid body collisions with friction , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[9]  W. Stronge.  Unraveling Paradoxical Theories for Rigid Body Collisions , 1991 .

[10]  Charles E. Smith.  Predicting Rebounds Using Rigid-Body Dynamics , 1991 .

[11]  R. Brach,et al.  Mechanical Impact Dynamics: Rigid Body Collisions , 1991 .

[12]  H. Cohen,et al.  Impulsive Motions of Elastic Pseudo-Rigid Bodies , 1991 .

[13]  Charles E. Smith,et al.  Coefficients of Restitution , 1992 .

[14]  M. T. Mason,et al.  Two-Dimensional Rigid-Body Collisions With Friction , 1992 .

[15]  James K. Mills,et al.  Robotic Manipulator Collisions: Modeling and Simulation , 1992 .

[16]  Joaquim A. Batlle,et al.  On Newtons and Poissons Rules of Percussive Dynamics , 1993 .

[17]  Mihail C. Roco,et al.  Particulate two-phase flow , 1993 .

[18]  J. Jaeger,et al.  Oblique impact of similar bodies with circular contact , 1994 .

[19]  Y. Hurmuzlu,et al.  Three-dimensional rigid-body collisions with multiple contact points , 1995 .

[20]  V. Bhatt,et al.  Three-Dimensional Frictional Rigid-Body Impact , 1995 .

[21]  A. Ivanov.  On multiple impact , 1995 .

[22]  B. Brogliato.  Nonsmooth Impact Mechanics: Models, Dynamics and Control , 1996 .

[23]  D. Stoianovici,et al.  A Critical Study of the Applicability of Rigid-Body Collision Theory , 1996 .

[24]  J. A. Batlle.  Rough Balanced Collisions , 1996 .

[25]  Discussion: “A Critical Study of the Applicability of Rigid-Body Collision Theory” (Stoianovici, D., and Hurmuzlu, Y., 1996, ASME J. Appl. Mech., 63, pp. 307–316) , 1997 .

[26]  A. Ruina,et al.  A New Algebraic Rigid-Body Collision Law Based on Impulse Space Considerations , 1998 .

[27]  Yildirim Hurmuzlu,et al.  An Energy-Based Coefficient of Restitution for Planar Impacts of Slender Bars With Massive External Surfaces , 1998 .

[28]  A. Ruina,et al.  Anomalous Frictional Behavior in Collisions of Thin Disks , 1999 .

[29]  J. Barbera,et al.  Contact mechanics , 1999 .