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On Solvability of Multibody Contact Problems

[+] Author Affiliations
Alexander P. Ivanov

Moscow State Textile University, Moscow, Russia

Paper No. DETC2007-34489, pp. 381-384; 4 pages
doi:10.1115/DETC2007-34489
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

The paper is devoted to dynamic multi-rigid-body contact problems with dry friction. It is known that such problem may have multiple solutions or none solution (so-called Painlevé paradoxes). A great deal of works concerning overcoming of the paradoxes was published last century, but general conditions of existence and uniqueness were not derived yet. We consider systems with a finite numbers of contact points with well-defined contact directions and Coulomb friction. The equations of motion contain unknowns of two kinds: the accelerations and the contact forces. According to the friction law, some of these variables vanish, and remaining ones can be treated as a coordinate system in the space of the generalized forces. Thus, this space splits to a finite number of regions with different coordinates. From a geometrical point of view, the solvability of the multi-contact problem means that the union of these regions equals to the whole space. Furthemore, the solution is unique ⇔ any pair of regions has empty intersection, and the coordinates within any region are defined uniquely. We present some algebraic conditions, which are equivalent to these geometric properties. Therefore, necessary and sufficient conditions of correct solution to multibody contact problem are obtained for the first time. A number of mechanical examples are considered to illustrate new results.

Copyright © 2007 by ASME

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