Journal of Nonlinear Science

, Volume 27, Issue 1, pp 241–283 | Cite as

Hamel’s Formalism for Infinite-Dimensional Mechanical Systems

  • Donghua Shi
  • Yakov Berchenko-Kogan
  • Dmitry V. Zenkov
  • Anthony M. Bloch
Article

Abstract

In this paper, we introduce Hamel’s formalism for infinite-dimensional mechanical systems and in particular consider its applications to the dynamics of nonholonomically constrained systems. This development is a nontrivial extension of its finite-dimensional counterpart. The analysis is applied to several continuum mechanical systems of interest, including coupled systems and systems with infinitely many constraints.

Keywords

Hamel equations Nonholonomic constraints Momentum Symmetry 

Mathematics Subject Classification

70F25 37J60 70H33 

Notes

Acknowledgments

We would like to thank Professors Yongxin Guo, Francois Gay-Balmaz, Vakhtang Putkaradze, and Tudor Ratiu for valuable discussions, and the reviewers for helpful remarks.

The research of AMB was partially supported by NSF Grants DMS-1207893, DMS-1613819, INSPIRE-1363720, and the Simons Foundations. The research of DS was partially supported by the China Scholarship Council. DS wishes to thank support and hospitality of North Carolina State University during his visit. The research of YBK was partially supported by NDSEG Fellowship. The research of DVZ was partially supported by NSF grants DMS-0908995 and DMS-1211454. DVZ would like to acknowledge support and hospitality of the Beijing Institute of Technology, where a part of this work was carried out.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  4. 4.Department of MathematicsUniversity of MichiganAnn ArborUSA

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