On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints

Hiroaki Yoshimura; Kenji Soya

doi:10.1115/DETC2009-86354

On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints

Hiroaki Yoshimura^*, Kenji Soya

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

This paper develops a discrete Hamiltonian system with holonomic constraints with Geometric Constraint Stabilization. It is first shown that constrained mechanical systems with nonconservative external forces can be formulated by using canonical symplectic structures in the context of Hamiltonian systems. Second, it is shown that discrete holonomic Hamiltonian systems can be developed via the discretization based on the Backward Differentiation Formula and also that geometric constraint stabilization can be incorporated into the discrete Hamiltonian systems. It is demonstrated that the proposed method enables one to stabilize constraint violations effectively in comparison with conventional methods such as Baumgarte Stabilization and Gear-Gupta-Leimkuhler Stabilization, together with an illustrative example of linkage mechanisms.

Original language	English
Title of host publication	Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
Pages	517-521
Number of pages	5
Edition	PART A
DOIs	https://doi.org/10.1115/DETC2009-86354
Publication status	Published - 2010 Jun 24
Event	2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009 - San Diego, CA, United States Duration: 2009 Aug 30 → 2009 Sept 2

Publication series

Name	Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
Number	PART A
Volume	4

Conference

Conference	2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009
Country/Territory	United States
City	San Diego, CA
Period	09/8/30 → 09/9/2

ASJC Scopus subject areas

Computer Networks and Communications
Hardware and Architecture
Electrical and Electronic Engineering

Access to Document

10.1115/DETC2009-86354

Cite this

Yoshimura, H., & Soya, K. (2010). On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009 (PART A ed., pp. 517-521). (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; Vol. 4, No. PART A). https://doi.org/10.1115/DETC2009-86354

On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. / Yoshimura, Hiroaki; Soya, Kenji.

Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A. ed. 2010. p. 517-521 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; Vol. 4, No. PART A).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yoshimura, H & Soya, K 2010, On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A edn, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009, no. PART A, vol. 4, pp. 517-521, 2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009, San Diego, CA, United States, 09/8/30. https://doi.org/10.1115/DETC2009-86354

Yoshimura H, Soya K. On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A ed. 2010. p. 517-521. (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; PART A). doi: 10.1115/DETC2009-86354

Yoshimura, Hiroaki ; Soya, Kenji. / On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A. ed. 2010. pp. 517-521 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; PART A).

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On the geometric stabilization for discrete Hamiltonian systems with holonomic constraints

Abstract

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