Numerical location of Painlev\'e paradox-associated jam and lift-off in a double pendulum mechanism

[+] Author and Article Information
Shane/J Burns

Institute for Infrastructure and Environment School of Engineering The University of Edinburgh Edinburgh EH9 3JL, UK

Petri Piiroinen

Lecturer in Applied Mathematics School of Mathematics, Statistics and Applied Mathematics National University of Ireland, Galway University Road, Galway, Ireland

1Corresponding author.

ASME doi:10.1115/1.4037033 History: Received November 02, 2016; Revised June 06, 2017


In this article we will introduce the phenomenon known as the Painlev\'e paradox, and further discuss the associated coupled phenomena, jam and lift-off. We analyse under what conditions the Painlev\'e 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 visualise jam and lift-off in a numerical simulation, we choose to use the 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 Painlev\'e 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 Painlev\'e paradox for relatively low coefficient of friction values, and second we will use the energetic impact law to numerically show the occurrence of the Painlev\'e paradox in a double pendulum system.

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