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Inverse problem with two-parametric families of planar orbits

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Abstract

As a possible extension of recent work we study the following version of the inverse problem in dynamics: Given a two-parametric familyf(x, y, b)=c of plane curves, find an autonomous dynamical system for which these curves are orbits.

We derive a new linear partial differential equation of the first order for the force componentsX(x, y) andY(x, y) corresponding to the given family. With the aid of this equation we find that, depending on the given functionf, the problem may or may not have a solution. Based on given criteria, we present a full classification of the various cases which may arise.

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Authors and Affiliations

  1. Department of Theoretical Mechanics, University of Thessaloniki, Greece

    George Bozis

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  1. George Bozis
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Bozis, G. Inverse problem with two-parametric families of planar orbits. Celestial Mechanics 31, 129–142 (1983). https://doi.org/10.1007/BF01686815

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  • DOI: https://doi.org/10.1007/BF01686815

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