Meccanica

, Volume 30, Issue 3, pp 271–289 | Cite as

The magnetic spherical pendulum

  • R. Cushman
  • L. Bates
Article

Abstract

This article gives two formulae for the rotation number of the flow of the magnetic spherical pendulum on a torus corresponding to a regular value of the energy momentum mapping. One of these formulae is nonclassical and is based on an idea of Montgomery.

Key words

Completely integrable system particle mechanics 

Sommario

In questo lavoro si danno due formule per il numero di rotazione del flusso del sferico pendolo magnetico su un toro che corrisponde a un valore regolare dell'applicazione energia-momento. Una di queste formule è nonclassica ed è basata su un'idea di Montgomery.

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References

  1. 1.
    Arms, J., Cushman, R., and Gotay, M., ‘A universal reduction procedure for Hamiltonian group actions’, in: T. Ratiu (Ed.),Geometry of Hamiltonian Systems, Springer-Verlag, New York, 1991, pp. 33–51.Google Scholar
  2. 2.
    Arnol'd, V.,Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, 1978.Google Scholar
  3. 3.
    Dirac, P.A.M.,Lectures on Quantum Mechanics, Academic Press, New York, 1964.Google Scholar
  4. 4.
    Cushman, R. and Knörrer, H., ‘The momentum mapping of the Lagrange top’, in: H. Doebner and J. Henning (Eds.),Differential Geometric Methods in Mathematical Physics, Lecture Notes in Mathematics, vol. 1139, Springer-Verlag, New York, 1985, pp. 12–24.Google Scholar
  5. 5.
    Cushman, R. and van der Meer, J.-C., ‘The Hamiltonian Hopf bifurcation in the Lagrange top’, in: Albert, C. (Ed.),Géométrie Symplectique et Mécanique, Lecture Notes in Mathematics, vol. 1416, Springer-Verlag, New York, 1991, pp. 26–38.Google Scholar
  6. 6.
    Montgomery, R., ‘How much does the rigid body rotate?’,American Journal of Physics,59 (1991) 394–398.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • R. Cushman
    • 1
  • L. Bates
    • 2
  1. 1.Mathematics InstituteRijksuniversiteit UtrechtUtrechtThe Netherlands
  2. 2.Department of MathematicsUniversity of CalgaryCalgaryCanada

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