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Poincaré-Cartan Integral Variants and Invariants of Nonholonomic Constrained Systems

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Abstract

Usually there does not exist an integral invariant of Poincaré-Cartan's type for a nonholonomic system because a constraint submanifold does not admit symplectic structure in general. An integral variant of Poincaré-Cartan's type, depending on the nonholonomy of the constraints and nonconservative forces acting on the system, is derived from D'Alembert-Lagrange principle. For some nonholonomic constrained mechanical systems, there exists an alternative Lagrangian which determines the symplectic structure of a constraint submanifold. The integral invariants can then be constructed for such systems.

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Authors and Affiliations

  1. Liaoning University, Shenyang, 110036, People's Republic of China

    Y. X. Guo

  2. Department of Applied Mechanics, Beijing Institute of Technology, Beijing, 100081, People's Republic of China

    M. Shang & F. X. Mei

  3. Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teacher's College, Shangqiu, 476000, People's Republic of China

    S. K. Luo

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  1. Y. X. Guo
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  2. M. Shang
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  3. S. K. Luo
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  4. F. X. Mei
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Correspondence to Y. X. Guo.

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Guo, Y.X., Shang, M., Luo, S.K. et al. Poincaré-Cartan Integral Variants and Invariants of Nonholonomic Constrained Systems. International Journal of Theoretical Physics 40, 1197–1205 (2001). https://doi.org/10.1023/A:1017565805424

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  • DOI: https://doi.org/10.1023/A:1017565805424

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