Variational Principles

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


This chapter introduces the variational principles of mechanics in the case of unilateral constraints and impacts. We start with virtual displacements and then proceed with variational inequalities formalisms (equivalently inclusions into normal cones to tangent cones and convex sets), Fourier and Jourdain’s principles. The second part is dedicated to the Lagrange dynamics. The case with exogenous impulsive forces is obtained from the material of Chap.  1. Hamilton’s principle, which is far more involved, is treated in the last part of the chapter. The chapter ends with some comments about the link with optimal control under state inequality constraints.


Contact Force Differential Inclusion Tangent Cone Virtual Displacement Impact Time 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.INRIA Rhône-AlpesSaint-IsmierFrance

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