An equation for the characteristic curve of a family of symmetric periodic orbits

Details An equation for the characteristic curve of a family of symmetric periodic orbits An equation for the characteristic curve of a family of symmetric periodic orbits

Aug 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cemda..59..301b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 59, no. 4, p. 301-311

Astronomy and Astrophysics

Astronomy

3

Celestial Mechanics, Circular Orbits, Elliptical Orbits, Orbital Mechanics, Astronomical Models, Celestial Reference Systems, Three Body Problem

Scientific paper

Szebehely's equation for the inverse problem of Dynamics is used to obtain the equation of the characteristic curve of a family f(x,y) = c of planar periodic orbits (crossing perpendicularly the x-axis) created by a certain potential V(x,y). Analytic expressions for the characteristic curves are found both in sideral and synodic systems. Examples are offered for both cases. It is shown also that from a given characteristic curve, associated with a given potential, one can obtain an analytic expression for the slope of the orbit at any point.

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