Abstract
We consider the following case of the 3D inverse problem of dynamics: Given a spatial two-parametric family of curves \(f(x,y,z)=c_{1},g(x,y,z)=c_{2}\), find possibly existing two-dimension potentials under whose action the curves of the family are trajectories for a unit mass particle. First we establish the
conditions which must be fulfilled by the family so that potentials of the form \(w(y,z)\) give rise to the curves of the family, and we present some applications. Then we examine briefly the existence of potentials depending on \((x,z)\), respectively \((x,y)\), which are compatible with the given family.
Authors
Mira Cristiana Anisiu
T. Popoviciu Institute of Numerical Analysis, Cluj-Napoca, Romania
George Bozis
Aristotle University of Thesaloniki, GR-54006, Greece
Keywords
celestial mechanics – stellar dynamics
Cite this paper as:
Anisiu, M-C., Bozis, G, Two-dimension potentials which generate spatial families of orbits, Astronomische Nachrichten, vol.330, issue 4, 2009, pag.411-415
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