2025/01/22 by Edward A. Turner, Turner, Edward A., Francisco Crespo +7
Engineering · Mathematics · Physics and Astronomy · #37J25 #70F10 #70H05 #70H09 #70H33 #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2501.13089
openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the motion in space of an infinitesimal particle in the gravitational field generated by three primary bodies positioned at the vertices of a fixed equilateral triangle. We assume that the distances between the primaries are small compared to their separation from the particle. By applying a Lie-Deprit normalization, we simplify the Hamiltonian, relegating both the mean anomaly and the argument of periapisis to third-order terms or higher. After reducing out the symmetries associated with the Kepler flow and the central action of the angular momentum, we examine the relative equilibria in the first and second reduced spaces. We are able to identify the conditions for the existence of circular periodic orbits and KAM tori, thus providing insight into the system's long-term stability and dynamic structure.