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

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.