Families of orbits in planar anisotropic fields

Details Families of orbits in planar anisotropic fields Families of orbits in planar anisotropic fields

Jan 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005an....326...75a&link_type=abstract

Astronomische Nachrichten, Vol.326, Issue 1, p.75-78

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Stellar Dynamics

Scientific paper

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(a2x2+y2), (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.

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