Special Families of Orbits in the Direct Problem of Dynamics

Details Special Families of Orbits in the Direct Problem of Dynamics Special Families of Orbits in the Direct Problem of Dynamics

Mar 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004cemda..88..245a&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 88, Issue 3, p. 245-257 (2004).

Astronomy and Astrophysics

Astronomy

Integrability, Inverse And Direct Problem Of Dynamics, Special Families Of Orbits

Scientific paper

The direct problem of dynamics in two dimensions is modeled by a nonlinear second-order partial differential equation, which is therefore difficult to be solved. The task may be made easier by adding some constraints on the unknown function γ = f y /f x , where f(x, y) = c is the monoparametric family of orbits traced in the xy Cartesian plane by a material point of unit mass, under the action of a given potential V(x, y). If the function γ is supposed to verify a linear first-order partial differential equation, for potentials V satisfying a differential condition, γ can be found as a common solution of certain polynomial equations.

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