中国物理B ›› 2001, Vol. 10 ›› Issue (1): 1-6.doi: 10.1088/1009-1963/10/1/301

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CANONICAL FORMULATION OF NONHOLONOMIC CONSTRAINED SYSTEMS

郭永新1, 黄海军1, 于莹2   

  1. (1)Department of Physics, Liaoning University, Shenyang 110036, China; (2)School of Science, Shenyang University of Technology, Shenyang 110023, China
  • 收稿日期:2000-05-21 修回日期:2000-06-16 出版日期:2001-01-15 发布日期:2005-07-11
  • 基金资助:
    Project supported by the Science Rearch Foundation of Liaoning Educational Commitee, China (Grant No. 990111004).

CANONICAL FORMULATION OF NONHOLONOMIC CONSTRAINED SYSTEMS

Guo Yong-xin (郭永新)a, Yu Ying (于莹)b, Huang Hai-jun (黄海军)a   

  1. a Department of Physics, Liaoning University, Shenyang 110036, China; b School of Science, Shenyang University of Technology, Shenyang 110023, China
  • Received:2000-05-21 Revised:2000-06-16 Online:2001-01-15 Published:2005-07-11
  • Supported by:
    Project supported by the Science Rearch Foundation of Liaoning Educational Commitee, China (Grant No. 990111004).

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摘要： Based on the Ehresmann connection theory and symplectic geometry, the canonical formulation of nonholonomic constrained mechanical systems is described. Following the Lagrangian formulation of the constrained system, the Hamiltonian formulation is given by Legendre transformation. The Poisson bracket defined by an anti-symmetric tensor does not satisfy the Jacobi identity for the nonintegrability of nonholonomic constraints. The constraint manifold can admit symplectic submanifold for some cases, in which the Lie algebraic structure exists.

Abstract: Based on the Ehresmann connection theory and symplectic geometry, the canonical formulation of nonholonomic constrained mechanical systems is described. Following the Lagrangian formulation of the constrained system, the Hamiltonian formulation is given by Legendre transformation. The Poisson bracket defined by an anti-symmetric tensor does not satisfy the Jacobi identity for the nonintegrability of nonholonomic constraints. The constraint manifold can admit symplectic submanifold for some cases, in which the Lie algebraic structure exists.

Key words: nonholonomic constraints, canonical formulation, Ehresmann connection, symplectic submanifold

中图分类号:  (Algebraic structures and number theory)

  • 02.10.De
02.30.Zz (Inverse problems) 02.40.Vh (Global analysis and analysis on manifolds)