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Motion of a rolling disk by a new generalized Hamilton-Jacobi method

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Summary

The rolling motion of a disk on a horizontal plane in a gravitational field is studied by applying a new generalized Hamilton-Jacobi method. This method covers systems subject to nonholonomic Chetaev's constraints and is based on a variational principle for the integral of action. The particular case of the uniform circular rolling of the disk is discussed in detail.

Résumé

Le roulement d'un disque sur un plan horizontal dans un champ gravitationnel est étudié en utilisant une nouvelle méthode généralisée de Hamilton-Jacobi. Cette méthode s'applique à des systèmes soumis à des contraintes non-holonomes du type de Chetaev et est basée sur un principe variationnel pour l'intégrale de l'action. Le cas particulier du roulement uniforme circulaire du disque est discuté en détail.

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References

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Authors and Affiliations

  1. Dept. of Analytical Mechanics, Vrije Universiteit Brussel, Brussels, Belgium

    René Van Dooren

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  1. René Van Dooren
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Van Dooren, R. Motion of a rolling disk by a new generalized Hamilton-Jacobi method. Journal of Applied Mathematics and Physics (ZAMP) 27, 501–505 (1976). https://doi.org/10.1007/BF01594907

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  • DOI: https://doi.org/10.1007/BF01594907

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