Isochrony in 3D Radial Potentials View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-10

AUTHORS

Alicia Simon-Petit, Jérôme Perez, Guillaume Duval

ABSTRACT

Revisiting and extending an old idea of Michel Hénon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They appear in spherically symmetrical systems formed by a large amount of charges (electrical or gravitational) of the same type considered in mean-field theory. Such potentials are defined by the fact that the radial period of a test charge in such potentials, provided that it exists, depends only on its energy and not on its angular momentum. Our characterization of the isochrone set is based on the action of a real affine subgroup on isochrone potentials related to parabolas in the R2 plane. Furthermore, any isochrone orbits are mapped onto associated Keplerian elliptic ones by a generalization of the Bohlin transformation. This mapping allows us to understand the isochrony property of a given potential as relative to the reference frame in which its parabola is represented. We detail this isochrone relativity in the special relativity formalism. We eventually exploit the completeness of our characterization and the relativity of isochrony to propose a deeper understanding of general symmetries such as Kepler’s Third Law and Bertrand’s theorem. More... »

PAGES

605-653

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-018-3212-y

DOI

http://dx.doi.org/10.1007/s00220-018-3212-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105760486


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