Inverse problem with two-parametric families of planar orbits

Details Inverse problem with two-parametric families of planar orbits Inverse problem with two-parametric families of planar orbits

Oct 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..31..129b&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 31, Oct. 1983, p. 129-142.

Astronomy and Astrophysics

Astronomy

21

Astrodynamics, Celestial Mechanics, Orbital Mechanics, Curves (Geometry), Linear Equations, Partial Differential Equations, Potential Fields

Scientific paper

As a possible extension of a recent work the author studies the following version of the inverse problem in dynamics: Given a two-parametric family f(x, y, b) = c of plane curves, find an autonomous dynamical system for which these curves are orbits. The author derives a new linear partial differential equation of the first order for the force components X(x, y) and Y(x, y) corresponding to the given family. With the aid of this equation he finds that, depending on the given function f, the problem may or may not have a solution. Based on given criteria, a fully classification of the various cases which may arise is presented.

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