Integrability and Bifurcation Analysis of the Problem of a Spherical Top Rolling on a Plane Without Spinning and with Partial Slipping

• Autores: Alexander A. Kilin, Tatiana B. Ivanova
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 5, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper addresses the problem of the rolling motion of a sphere with axisymmetric mass distribution on a horizontal plane. It is assumed that the sphere does not slip as it rolls in the direction of the projection of the symmetry axis onto the supporting plane, and that there is no spinning relative to the vertical. For the system under consideration, integrals of motion are found, a reduction to a system with one degree of freedom is performed, and the equations of motion of the reduced system are written in Hamiltonian form. A classification of possible types of motion according to the values of first integrals of motion and mass-geometric parameters is presented, and the singularities of the system and the dynamical effects observed near them are described. Special attention is given to the particular case of a balanced sphere for which the bifurcation diagram in the space of first integrals is fairly simple and illustrative, but retains its singularities associated with the degeneracy of the system of nonholonomic constraints.

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