2018/04/28 by Martı́n Lara, Martin Lara · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Astro and Planetary Science #Classical mechanics #Computation #Geometry #Libration (molecule) #Mathematical analysis #Mathematics #Nonlinear system #Perturbation (astronomy) #Physics #Point (geometry) #Space Satellite Systems and Control #Spacecraft Dynamics and Control #Trigonometric functions #Trigonometry #astro-ph.EP #math.DS
paper · pdf · doi:10.1007/s11071-018-4304-0
published as Nonlinear Dynamics, on line (April 28, 2018) · 42 pages, 16 figures
openalex publication_date 2018/04/28 · arxiv created 2018/07/16 · arxiv updated 2018/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The non-integrability of the Hill problem makes that its global dynamics must be necessarily approached numerically. However, the analytical approach is feasible in the computation of relevant solutions. In particular, the nonlinear dynamics of the Hill problem close to the origin, and the libration point dynamics have been thoroughly investigated by perturbation methods. Out of the Hill sphere, the analytical approach is also feasible, at least in the case of distant retrograde orbits. Previous analytical investigations of this last case succeeded in the qualitative description of the dynamics, but they commonly failed in providing accurate results. This is a consequence of the essential dependance of the dynamics on elliptic functions, a fact that makes to progress in the perturbation approach beyond the lower orders of the solution really difficult. We propose an alternative perturbation approach that allows us to provide a very simple low order analytical solution in trigonometric functions, on the one hand, and, while still depending on special functions, to compute higher orders of the solution, on the other.