Advanced Topics in Nonsmooth Dynamics by Remco Leine Vincent Acary & Olivier Brüls

Author:Remco Leine, Vincent Acary & Olivier Brüls
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The domain of M is, by definition,

Hence, the law T assigns at each the section and the inverse law assigns to each the section . Let a constitutive law be given by a graph M. Does it admit a bipotential? The existence problem is easily settled by the following result.

Theorem 3.1

Given a non-empty set , there is a bipotential b such that if, and only if, for any and , the sections and are convex and closed.

The proof can be found in [4]. Then, we say that M is bi-convex and bi-closed, or in short, that M is a BB-graph. This criterion, simple to verify, allows for straightaway moving laws without bipotential aside. If the law is represented by a BB-graph, a closely related topic is to know whether the bipotential is unique. The answer is no. The proof of the previous result is based on the introduction of the bipotential

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.