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Rigid-body dynamics with friction and impact. (English) Zbl 0962.70010
The author discusses recent work on the theories of friction and impact, there being much more to them than the simple expressions, \(F\leq\mu N\) and \(v_1-v_2= -e(u_1-u_2)\). The paper opens with a discussion of Coulomb law and the Painlevé problem of a moving rod in contact with a rough surface. The author points out the usefulness of complementarity approach, and suggests that the concept of measure-differential inclusions can prove useful. From the numerical point of view, the author feels that a time stepping formulation using complimentarity conditions or optimisation to resolve whether contact is maintained or broken is the most useful, and applies this method to the Painlevé problem and to a billiard problem. The author also discusses the convergence of numerical solutions and points out that, in some cases, non-uniqueness can arise as a result of instability in stiff approximations.
Next, the possibility of regarding rigid body dynamics as a singular perturbation theory for stiff elastic bodies is mentioned together with the possible use of symplectic integrators. Amongst other matters, discussed are the difference between static and dynamic friction, and multiple contacts and impacts. There are over 140 references.

70E55 Dynamics of multibody systems
70F40 Problems involving a system of particles with friction
70F35 Collision of rigid or pseudo-rigid bodies
74M15 Contact in solid mechanics
70-02 Research exposition (monographs, survey articles) pertaining to mechanics of particles and systems
70-08 Computational methods for problems pertaining to mechanics of particles and systems
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