Physics of Particles and Nuclei Letters

, Volume 5, Issue 3, pp 278–281 | Cite as

Asymptotic Hamiltonian reduction for the dynamics of a particle on a surface

  • V. L. Golo
  • D. O. Sinitsyn


We consider the motion of a particle on the surface generated by a small perturbation of the standard sphere. The key observation is that a trajectory of the particle has the shape of a coil, and one may qualitatively describe the turns of the latter as a precessing great circle of the sphere. Thus, we change the configuration space of the initial problem for the space of great circles on the sphere. The construction enables us to derive a subsidiary Hamiltonian system having the shape of equations for the top with a 4th order Hamiltonian. The subsidiary system provides a detailed asymptotic description of the particle’s motion in terms of graphs on the standard sphere.

PACS numbers

02.60.Cb 11.10.Ef 


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  1. 1.
    E. T. Whittaker, A Treatise on the Analytical Dynamics (Cambridge Univ., Cambridge, 1927), Chs. III, IV, and XIII.MATHGoogle Scholar
  2. 2.
    C. G. Jacobi, Lectures on Dynamics (URSS, Moscow, 2004), Ch. 28.Google Scholar
  3. 3.
    R. W. Hamming, Numerical Methods for Scientists and Engineers (McGraw-Hill, New York, 1962), Ch. 24.MATHGoogle Scholar
  4. 4.
    E. J. Routh, Dynamics of a System of Rigid Bodies (McMillan, London, New York, 1891), Ch. 1.MATHGoogle Scholar
  5. 5.
    V. I. Arnold, Mathematical Methods in Classical Mechanics (Springer, New York, 1992), Ch. 9.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • V. L. Golo
    • 1
  • D. O. Sinitsyn
    • 1
  1. 1.Moscow State UniversityMoscowRussia

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