A perturbation method and some applications |
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Authors: | Alex Konopliv |
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Institution: | (1) Jet Propulsion Laboratory, California Institute of Technology, 91109 Pasadena, CA, USA |
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Abstract: | 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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