Abstract
We consider the problem : Given a planar region \(T_{orb}\) described by one inequality \(g(x,y)\leq c_{0}\), find the potentials \(V=V(x,y)\) which can generate monoparametric families of orbits \(f(x,y)=c\) (also to be found) lying exclusively in the region \(T_{orb}\). We make assumptions on the homogeneity of both the function \(g(x,y)\) describing the boundary of the region \(T_{orb}\) and of the slope function \(\U{3b3} (x,y)=fy/fx\) of the required family. We show that, under certain conditions, the slope function \(\U{3b3} (x,y)\) can be obtained as the common solution of two algebraic equations. The theoretical results are illustrated by an example.
Authors
George Bozis
Department of Physics, University of Thessaloniki, GR-54006, Greece
Mira-Cristiana Anisiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Keywords
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Paper coordinates
G. Bozis, M.-C. Anisiu, Programmed motion with homogeneity assumptions, Proceedings of the International Conference on the Dynamics of Celestial Bodies, 23-26 June 2008, Litohoro-Olympus, Thessaloniki, Greece, Eds. H. Varvoglis and Z. Knezevic, Beograd 2009, 83-87 (ISBN 978-960-243-664-6) (pdf file here)
About this paper
Journal
Publications of the Astronomical Observatory
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DOI
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Online ISSN
0373-3742
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