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Analysis of an oscillatory Painlevé-Klein apparatus with a nonholonomic constraint

Wagner, A. and Heffel, Eduard and Arrieta, A. F. and Spelsberg-Korspeter, G. and Hagedorn, P. (2013):
Analysis of an oscillatory Painlevé-Klein apparatus with a nonholonomic constraint.
In: Differential Equations and Dynamical Systems, pp. 149-157, 21, (1&2), [Article]

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Abstract

In dynamics, both the concepts of rigid body and Coulomb’s law of friction are well established, although it is known at least since Painlevé’s time that they may lead to irregularities and contradictions, such as loss of uniqueness or existence of the solution of the equations of motion. The problem is still of very actual interest, since it can be of practical significance also for the industrially used rigid body codes. One of the simplest mechanical systems in which these difficulties can be well described is the Painlevé–Klein apparatus. As most other systems discussed in this context in the literature, this is a holonomic system. In the present note, we briefly examine a nonholonomic oscillatory system which is an extension of the classical Painlevé–Klein apparatus and we study its dynamics with respect to the Painlevé paradox. Both the borders of paradoxical regions and their reachability are addressed.

Item Type: Article
Erschienen: 2013
Creators: Wagner, A. and Heffel, Eduard and Arrieta, A. F. and Spelsberg-Korspeter, G. and Hagedorn, P.
Title: Analysis of an oscillatory Painlevé-Klein apparatus with a nonholonomic constraint
Language: English
Abstract:

In dynamics, both the concepts of rigid body and Coulomb’s law of friction are well established, although it is known at least since Painlevé’s time that they may lead to irregularities and contradictions, such as loss of uniqueness or existence of the solution of the equations of motion. The problem is still of very actual interest, since it can be of practical significance also for the industrially used rigid body codes. One of the simplest mechanical systems in which these difficulties can be well described is the Painlevé–Klein apparatus. As most other systems discussed in this context in the literature, this is a holonomic system. In the present note, we briefly examine a nonholonomic oscillatory system which is an extension of the classical Painlevé–Klein apparatus and we study its dynamics with respect to the Painlevé paradox. Both the borders of paradoxical regions and their reachability are addressed.

Journal or Publication Title: Differential Equations and Dynamical Systems
Volume: 21
Number: 1&2
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Dynamics and Vibrations
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Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
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Date Deposited: 28 May 2014 12:51
Identification Number: doi:10.1007/s12591-012-0131-9
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