The planar inverse problem with four monoparametric families of curves

Details The planar inverse problem with four monoparametric families of curves The planar inverse problem with four monoparametric families of curves

Jun 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983a%26a...122..251x&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 122, no. 1-2, June 1983, p. 251-254.

Astronomy and Astrophysics

Astrophysics

5

Celestial Mechanics, Gravitational Fields, Orbital Mechanics, Solar System, Asteroids, Curves (Geometry), Kepler Laws, Satellite Orbits

Scientific paper

Necessary and sufficient conditions are obtained for the following version of the inverse problem: four monoparametric families of planar curves are orbits of a unit mass, moving in an autonomous (not necessarily conservative) force field, in a dynamical system with two degrees of freedom. It is found that, in the generic case, the forces are obtained essentially uniquely. As an application, Newton's law of gravitation is derived from four given co-planar and co-focal families of ellipses; the major axis is taken as the parameter along each family, whereas all members of each family have the same eccentricity and orientation.

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