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arXiv · 2408.04298

Mathieu equation as a result of Laplace perturbation theory in the restricted three body problem

Alexey Rosaev·Eva Plavalova
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Abstract

Linear equations with periodic coefficients describe the behavior of various dynamical systems. This studying is devoted to their applications to the planetary restricted three-body problem (RTBP). Here we consider the Laplace method for determining perturbation in coordinates. We show that classical theory of perturbation leads to a linear equation with periodic coefficients. Than we present a modification of Laplace method. This modification allows us to study motion over a longer time interval.

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Alexey Rosaev, Eva Plavalova. 2024-08-08. Mathieu equation as a result of Laplace perturbation theory in the restricted three body problem. https://arxiv.org/abs/2408.04298

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