Premium
Families of orbits in planar anisotropic fields
Author(s) -
Anisiu M.C.,
Bozis G.
Publication year - 2005
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.200410259
Subject(s) - anisotropy , planar , physics , action (physics) , inverse , class (philosophy) , point (geometry) , quantum , unit (ring theory) , mathematical physics , classical mechanics , theoretical physics , quantum mechanics , mathematics , geometry , computer science , computer graphics (images) , mathematics education , artificial intelligence
The aim of the planar inverse problem of dynamics is: given a monoparametric family of curves f ( x , y ) = c , find the potential V ( x , y ) under whose action a material point of unit mass can describe the curves of the family. In this study we look for V in the class of the anisotropic potentials V ( x , y ) = v ( a 2 x 2 + y 2 ), ( a =constant). These potentials have been used lately in the search of connections between classical, quantum, and relativistic mechanics. We establish a general condition which must be satisfied by all the families produced by an anisotropic potential. We treat special cases regarding the families (e. g. families traced isoenergetically) and we present certain pertinent examples of compatible pairs of families of curves and anisotropic potentials. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)