Translator Disclaimer
2019 Mechanics of Infinitesimal Test Bodies on Delaunay Surfaces: Spheres and Cylinders as Limits of Unduloids and Their Action-Angle Analysis
Vasyl Kovalchuk, Barbara Gołubowska, Ivaïlo Mladenov
J. Geom. Symmetry Phys. 53(none): 55-84 (2019). DOI: 10.7546/jgsp-53-2019-55-84

Abstract

This paper discusses the motion of infinitesimal gyroscopes along the two-dimensional surfaces of constant mean curvature embedded into the three-dimensional Euclidean space. We have considered the cases of unduloids, spheres, and cylinders for which the corresponding Hamilton-Jacobi equations are written and analyzed with the help of the action-angle variables. Spheres and cylinders are considered as limiting cases of unduloids and the residue analysis was performed which provides the connection between all three action variables and the energy. This has been traced also for the geodetic situations and for two additional classical model potentials.

Citation

Download Citation

Vasyl Kovalchuk. Barbara Gołubowska. Ivaïlo Mladenov. "Mechanics of Infinitesimal Test Bodies on Delaunay Surfaces: Spheres and Cylinders as Limits of Unduloids and Their Action-Angle Analysis." J. Geom. Symmetry Phys. 53 55 - 84, 2019. https://doi.org/10.7546/jgsp-53-2019-55-84

Information

Published: 2019
First available in Project Euclid: 28 October 2019

zbMATH: 1434.53009
MathSciNet: MR3971649
Digital Object Identifier: 10.7546/jgsp-53-2019-55-84

Rights: Copyright © 2019 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

JOURNAL ARTICLE
30 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Back to Top