Global projections for variational nonsmooth mechanics

David Pekarek*, Todd D. Murphey

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations

Abstract

This paper improves the projected Hamilton's principle (PHP) formulation of nonsmooth mechanics. Central to the PHP is the use of a projection mapping, defined on the configuration space, to capture nonsmooth behaviors. To support applications of the PHP with multiple impact times and locations, we define mild topological assumptions under which nonsmooth mechanical systems can be transformed to a prescribed normal form. In normal form coordinates, we provide a globally valid projection for use in the PHP. For systems that do not permit the transformation to normal form, we examine the use of constrained coordinates and incorporate holonomic constraints into the PHP. Lastly, as a preview of future developments of the PHP, we discuss the application of the method on compact manifolds.

Original languageEnglish (US)
Article number6426055
Pages (from-to)5572-5579
Number of pages8
JournalProceedings of the IEEE Conference on Decision and Control
DOIs
StatePublished - 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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