On the adelphic potentials compatible with a set of planar orbits |
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Authors: | Bálint Érdi George Bozis |
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Institution: | (1) Department of Astronomy, Eötvös University, Budapest, Hungary;(2) Department of Theoretical Mechanics, University of Thessaloniki, GR-540 06 Thessaloniki, Greece |
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Abstract: | Given a planar potentialB=B(x, y), compatible with a monoparametric family of planar orbitsf(x, y)=c, we face the problem of producing potentialsA=A(x, y), adelphic toB(x, y), i.e. nontrivial potentials which have in common withB(x, y) the given set of orbits. We establish a linear, second order partial differential equation for a functionP(x, y) and we prove that, to any definite positive solution of this equation, there corresponds a potentialA(x, y) adelphic toB(x, y). |
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Keywords: | Inverse problem of Dynamics adelphic potentials |
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