### Abstract

The paper Illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d'Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d'Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.

Original language | English |
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Title of host publication | Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005 |

Pages | 627-633 |

Number of pages | 7 |

Volume | 6 A |

Publication status | Published - 2005 |

Event | DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA Duration: 2005 Sep 24 → 2005 Sep 28 |

### Other

Other | DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference |
---|---|

City | Long Beach, CA |

Period | 05/9/24 → 05/9/28 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005*(Vol. 6 A, pp. 627-633)

**On the lagrangian formalism of nonholonomic mechanical systems.** / Yoshimura, Hiroaki.

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

*Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005.*vol. 6 A, pp. 627-633, DETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, 05/9/24.

}

TY - GEN

T1 - On the lagrangian formalism of nonholonomic mechanical systems

AU - Yoshimura, Hiroaki

PY - 2005

Y1 - 2005

N2 - The paper Illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d'Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d'Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.

AB - The paper Illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d'Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d'Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.

UR - http://www.scopus.com/inward/record.url?scp=33244469078&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33244469078&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33244469078

SN - 0791847438

VL - 6 A

SP - 627

EP - 633

BT - Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005

ER -