In this article, we will introduce the phenomenon known as the Painlevé paradox and further discuss the associated coupled phenomena, jam and lift-off. We analyze under what conditions the Painlevé paradox can occur for a general two-body collision using a framework that can be easily used with a variety of impact laws, however, in order to visualize jam and lift-off in a numerical simulation, we choose to use a recently developed energetic impact law as it is capable of achieving a unique forward solution in time. Further, we will use this framework to derive the criteria under which the Painlevé paradox can occur in a forced double-pendulum mechanical system. First, using a graphical technique, we will show that it is possible to achieve the Painlevé paradox for relatively low coefficient of friction values, and second we will use the energetic impact law to numerically show the occurrence of the Painlevé paradox in the double-pendulum system.
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November 2017
Research-Article
Numerical Location of Painlevé Paradox-Associated Jam and Lift-Off in a Double-Pendulum Mechanism
Shane J. Burns,
Shane J. Burns
Institute for Infrastructure and Environment,
School of Engineering,
The University of Edinburgh,
Edinburgh EH9 3JL, UK
e-mail: shane.burns111@gmail.com
School of Engineering,
The University of Edinburgh,
Edinburgh EH9 3JL, UK
e-mail: shane.burns111@gmail.com
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Petri T. Piiroinen
Petri T. Piiroinen
School of Mathematics,
Statistics and Applied Mathematics,
National University of Ireland, Galway,
University Road,
Galway H91 TK33, Ireland
e-mail: petri.piiroinen@nuigalway.ie
Statistics and Applied Mathematics,
National University of Ireland, Galway,
University Road,
Galway H91 TK33, Ireland
e-mail: petri.piiroinen@nuigalway.ie
Search for other works by this author on:
Shane J. Burns
Institute for Infrastructure and Environment,
School of Engineering,
The University of Edinburgh,
Edinburgh EH9 3JL, UK
e-mail: shane.burns111@gmail.com
School of Engineering,
The University of Edinburgh,
Edinburgh EH9 3JL, UK
e-mail: shane.burns111@gmail.com
Petri T. Piiroinen
School of Mathematics,
Statistics and Applied Mathematics,
National University of Ireland, Galway,
University Road,
Galway H91 TK33, Ireland
e-mail: petri.piiroinen@nuigalway.ie
Statistics and Applied Mathematics,
National University of Ireland, Galway,
University Road,
Galway H91 TK33, Ireland
e-mail: petri.piiroinen@nuigalway.ie
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 2, 2016; final manuscript received June 6, 2017; published online September 7, 2017. Assoc. Editor: Stefano Lenci.
J. Comput. Nonlinear Dynam. Nov 2017, 12(6): 061007 (8 pages)
Published Online: September 7, 2017
Article history
Received:
November 2, 2016
Revised:
June 6, 2017
Citation
Burns, S. J., and Piiroinen, P. T. (September 7, 2017). "Numerical Location of Painlevé Paradox-Associated Jam and Lift-Off in a Double-Pendulum Mechanism." ASME. J. Comput. Nonlinear Dynam. November 2017; 12(6): 061007. https://doi.org/10.1115/1.4037033
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