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Impulsive Dynamics and Measure Differential Equations

  • Bernard BrogliatoEmail author
Chapter
Part of the Communications and Control Engineering book series (CCE)

Abstract

This chapter is devoted to introducing the mathematical basis on which various evolution problems involving impulsive terms rely. Impulsive forces in mechanics are first presented disregarding what they may be produced by. It is shown on simple examples why impulsive mechanics involves only measures (Dirac “functions”), and no distribution of higher degree (derivatives of the Dirac “function”). Various classes of measure differential equations (MDEs), or impulsive systems, are introduced. Then unilaterally constrained dynamical systems are presented, and the differences with the foregoing MDEs are discussed. Variable changes that allow one to transform MDEs into Carathéodory ordinary differential equations (ODEs) or unilaterally constrained mechanical systems into Filippov’s differential inclusions, are described in the last section.

Keywords

Vector Field Differential Inclusion Linear Complementarity Problem Continuous Dependence Impulsive System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.INRIA Rhône-AlpesSaint-IsmierFrance

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