Mechanics of the Infinitesimal Gyroscopes on the Mylar Balloons and Their Action-Angle Analysis

Abstract

Here we apply the general scheme for description of the mechanics of infinitesimal bodies in the Riemannian spaces to the examples of geodetic and non-geodetic (for two different model potentials) motions of infinitesimal rotators on the Mylar balloons. The structure of partial degeneracy is investigated with the help of the corresponding Hamilton-Jacobi equation and action-angle analysis. In all situations it was found that for any of the six disjoint regions in the phase space among the three action variables only two of them are essential for the description of our models at the level of the old quantum theory (according to the Bohr-Sommerfeld postulates). Moreover, in both non-geodetic models the action variables were intertwined with the quantum number $N$ corresponding to the quantization of the radii $r$ of the inflated Mylar balloons.

arXiv comment15 pages, 2 figures

References in corpus (4)

• Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media
• Constraints and symmetry in mechanics of affine motion
• On Classical Dynamics of Affinely-Rigid Bodies Subject to the Kirchhoff-Love Constraints
• Dynamical systems with internal degrees of freedom in non-Euclidean spaces

Cited by in corpus (1)

• Mechanics of Incompressible Test Bodies Moving in Riemannian Spaces