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Numerical aspects of the sweeping process. (English) Zbl 0968.70006

The paper opens with brief descriptions of event-driven methods and contact dynamics. These are followed by a description of the sweeping process and of its application to a set moving by translation and to the finite intersection of smoothly moving regions. The author then discusses existence theorems and the idea of weak solutions. He points out that, in order to discuss a mechanical system, it is necessary to introduce an appropriate set of generalized coordinates, and that for contact kinematic inequalities may be needed to express the non-interpenetration of two bodies.
Next the ideas of frictionless contact dynamics are introduced. There is a discussion of expressing non-interpenetration in terms of velocities, and it is shown that the solution of this problem is equivalent to the solution of a quadratic programming problem for velocities. The concept of non-interpenetration is considered in terms of accelerations, and the idea of contact is examined in detail. Finally, collisions are discussed in detail. There is also a long list of references.
The tone of the paper is abstract, and there are not any examples of applications of the theory to physical situations.

MSC:

70-08 Computational methods for problems pertaining to mechanics of particles and systems
70E99 Dynamics of a rigid body and of multibody systems
70B99 Kinematics
70F35 Collision of rigid or pseudo-rigid bodies
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