Singular limits for impulsive lagrangian systems with dissipative sources

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Scopus citations

Abstract

Consider a mechanical system, described by finitely many Lagrangian coordinates. Assume that an external controller can influence the evolution of the system by directly assigning the values of some of the coordinates. If these assignments are implemented by means of frictionless constraints, one obtains a set of ordinary differential equations where the right hand side depends also on the time derivatives of the control functions. Some basic aspects of the mathematical theory for these equations are reviewed here. We then consider a system with an additional dissipative term, which vanishes on a stable submanifold N. As the coefficient of the source term approaches infinity, we show that the limiting impulsive dynamics on the reduced state space N can be modelled by two different systems, depending on the order in which two singular limits are taken. These results are motivated by the analysis of impulsive systems with non-holonomic constraints.

Original languageEnglish (US)
Title of host publicationProgress in Nonlinear Differential Equations and Their Application
PublisherSpringer US
Pages79-103
Number of pages25
DOIs
StatePublished - Jan 1 2008

Publication series

NameProgress in Nonlinear Differential Equations and Their Application
Volume75
ISSN (Print)1421-1750
ISSN (Electronic)2374-0280

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mechanics
  • Mathematical Physics
  • Control and Optimization
  • Applied Mathematics

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