A geometric approach to constraint stabilization for holonomic lagrangian systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

In this paper, we develop a geometric approach to constraint stabilization for holonomic mechanical systems in the context of Lagrangian formulation. We first show that holonomic mechanical systems, for the case in which a given Lagrangian is hyperregular, can be formulated by using the Lagrangian two-form, namely, a symplectic structure on the tangent bundle of a configuration manifold that is induced from the cotangent bundle via the Legendre transformation. Then, we present an idea of geometric constraint stabilization and we show that a holonomic Lagrangian system with geometric constraint stabilization can be formulated by the Lagrange-d'Alembert principle, together with its local coordinate expression for the sake of numerical computations. Finally, we illustrate the numerical verification that the proposed method enables to stabilize constraint violations effectively in comparison with the Baumgarte and Gear-Gupta-Leimkuhler methods together with an example of a linkage mechanism.

Original languageEnglish
Title of host publication2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Pages659-666
Number of pages8
DOIs
Publication statusPublished - 2008 Jun 17
Event6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 - Las Vegas, NV, United States
Duration: 2007 Sep 42007 Sep 7

Publication series

Name2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Volume5 PART A

Conference

Conference6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
CountryUnited States
CityLas Vegas, NV
Period07/9/407/9/7

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ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Mechanical Engineering
  • Modelling and Simulation

Cite this

Yoshimura, H. (2008). A geometric approach to constraint stabilization for holonomic lagrangian systems. In 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007 (pp. 659-666). (2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007; Vol. 5 PART A). https://doi.org/10.1115/DETC2007-35429