2022/11/02 by Guowei Yu, Yu, Guowei
Engineering · Physics and Astronomy · #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #Nuclear physics research studies #Spacecraft Dynamics and Control
paper · pdf · doi:10.48550/arxiv.2211.00916
openalex publication_date 2022/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Consider the planar restricted (N+1)-body problem with trajectories of the N(≥ 2) primaries forming a collision-free periodic solution of the N-body problem, for any positive energy h and directions θ± ∈ [0, 2π), we prove that starting from any initial position x at any initial time tx, there are hyperbolic solutions γ±|[tx, ± ∞) satisfying γ±(tx) =x and limt → ± ∞ γ±(t) / |γ±(t)| = e^i θ± (mod 2π), lim t → ± ∞ γ±(t) = ± √(2h) e^i θ± (mod 2π). Moreover we also prove the existence of a bi-hyperbolic solution γ|ℝ satisfying limt → ± ∞ γ(t) / |γ(t)| = e^i θ± (mod 2π), lim t → ± ∞ γ(t) = ± √(2h) e^i θ± (mod 2π).