A perturbation method and some applications

Details A perturbation method and some applications A perturbation method and some applications

Dec 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..47..305k&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 47, Issue 4, pp.305-320

Astronomy and Astrophysics

Astronomy

Scientific paper

For differential equations with one fast variable, a perturbation method is introduced that transforms a solution valid over only a short time interval to a new solution composed of averaged variables plus a periodic function of the averaged variables. The averaged variables are governed by a set of differential equations where the fast variable has been removed and thus can be numerically integrated quickly or solved directly. This method is applied to a perturbed harmonic oscillator with a cubic perturbation, van der Pol's equation, coorbital motion in the restricted three-body problem, and to nearly circular motion of a particle near one of the primaries in the restricted three-body problem.

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