2019/01/01 by Luis García-Naranjo, García-Naranjo, Luis, James Montaldi +1
Engineering · Physics and Astronomy · #70F05 #Astro and Planetary Science #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control
paper · doi:10.48550/arxiv.1906.01070
openalex publication_date 2019/01/01 · openalex created_date 2020/07/10 · openalex updated_date 2026/07/28
We first provide a classification of the pure rotational motion of 2\nparticles on a sphere interacting via a repelling potential. This is achieved\nby providing a simple geometric equivalence between repelling particles and\nattracting particles, and relying on previous work on the similar\nclassification for attracting particles. The second theme of the paper is to\nstudy the 2-body problem on a surface of constant curvature treating the\ncurvature as a parameter, and with particular interest in how families of\nrelative equilibria and their stability behave as the curvature passes through\nzero and changes sign. We consider two cases: firstly one where the particles\nare always attracting throughout the family, and secondly where they are\nattracting for negative curvature and repelling for positive curvature,\ninterpolated by no interaction when the curvature vanishes. Our analysis\nclarifies the role of curvature in the existence and stability of relative\nequilibria.\n