Mechanics of infinitesimal gyroscopes on Mylar balloons and their action‐angle analysis

Here, we apply the general scheme for description of mechanics of infinitesimal bodies in Riemannian spaces to the example of geodetic and non‐geodetic (for two different model potentials) motions of infinitesimal rotators on the Mylar balloon. The structure of partial degeneracy is investigated wit...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2020-04, Vol.43 (6), p.3040-3051
Main Authors: Kovalchuk, Vasyl, Mladenov, Ivailo M.
Format: Article
Language:English
Subjects:
action‐angle analysis
affinely rigid bodies
Balloons
Bohr‐Sommerfeld quantum theory
Gyroscopes
Hamilton‐Jacobi equation
infinitesimal gyroscopes
Mechanics (physics)
Mylar
Mylar balloons
Quantum theory
residue analysis
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Summary:Here, we apply the general scheme for description of mechanics of infinitesimal bodies in Riemannian spaces to the example of geodetic and non‐geodetic (for two different model potentials) motions of infinitesimal rotators on the Mylar balloon. 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 sixth disjoint regions in the phase space among the three action variables only two 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 quantized value of the radius r of the inflated Mylar balloon.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.6099