Analytical Solution for Third-Body Perturbations with Double Averaging

What is it about?

The doubly-averaged dynamical model is capable of predicting the long-term evolution of orbital elements, even in scenarios where the perturbing body traverses an inclined orbit. In this work, orbital dynamics perturbed by an inclined body have been simplified using a coordinate transformation, and the analytical solution for the doubly-averaged dynamics based on two integrals and Jacobi elliptic functions has been derived. This analytical solution is applicable to both circulating and librating patterns. In addition, the long-term evolution of the inclination can be determined accurately even in cases where the relative angle between the orbital planes of the perturbed orbiter and the perturbing body is larger than $39.23^{\circ}$. Simulation results have validated the accuracy of the analytical solution.

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