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The Planar Inverse Problem for Autonomous Systems

Published online by Cambridge University Press:  12 April 2016

Basilis C. Xanthopoulos  and
George Bozis
Basilis C. Xanthopoulos
Affiliation:
Astronomy Department, University of Thessaloniki, Thessaloniki and Department of Physics, University of Crete, Iraklion, Greece
George Bozis
Affiliation:
Department of Theoretical Mechanics, University of Thessaloniki, Thessaloniki, Greece

Abstract

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We study the general version of the inverse problem for planar trajectories and for autonomous dynamical systems possessing three integrals, i.e., for a given three-parametric family of curves f(x,y,a,b)=c we find the potential V(x,y) for which these curves are orbits of a unit mass. All possible cases, depending on the preassigned function f, are classified and in each case the necessary and sufficient conditions for the.existence of a solution are established. Among the examples is the case of the Keplerian conic sections which is studied in detail.

Type
Part VI - Miscellaneous Dynamics
Information
International Astronomical Union Colloquium , Volume 74: Dynamical Trapping and Evolution in the Solar System , 1983 , pp. 353 - 367
Copyright
Copyright © Reidel 1983

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