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The conditions for the unique solvability of the equations of the dynamics of systems with friction

✍ Scribed by A.P. Ivanov

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
404 KB
Volume
72
Category
Article
ISSN
0021-8928

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✦ Synopsis

The problem of determining the generalized accelerations and reactions of constraints in systems with dry friction is investigated. The necessary and sufficient conditions for the unique solvability of the problem are obtained, applicable for cases of sliding and static friction. A geometrical approach is used, based on the introduction of a certain auxiliary parameter space divided into non-overlapping regions in terms of the number of possible types of motion. In each of these regions there are explicit expressions for the accelerations and reactions, which enable us, using piecewise-smooth mapping, to express, from the equations of motion, the generalized forces in terms of the parameters. The solution of the problem is equivalent to inverting the given mapping. A number of examples are given.

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