2020/11/18 by Luca Asselle, Marco Fenucci, Asselle, Luca +4
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Bifurcation #Classical mechanics #Combinatorics #Computer science #Constant (computer programming) #Continuation #Cosmology and Gravitation Theories #Dimension (graph theory) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry #Geophysics and Gravity Measurements #Mathematical analysis #Mathematics #Newtonian fluid #Nonlinear system #Orbit (dynamics) #Physics #Pure mathematics #Simple (philosophy) #Spacecraft Dynamics and Control #Three-body problem #math.DS #n-body problem
paper · pdf · doi:10.48550/arxiv.2011.09291
18 pages, 3 figures. Comments welcome
arxiv created 2020/11/18 · openalex publication_date 2020/11/18 · arxiv updated 2020/11/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/08/05
For the gravitational n-body problem, the simplest motions are provided by those rigid motions in which each body moves along a Keplerian orbit and the shape of the system is a constant (up to rotations and scalings) configuration featuring suitable properties. While in dimension d ≤ 3 the configuration must be central, in dimension d ≥ 4 new possibilities arise due to the complexity of the orthogonal group, and indeed there is a wider class of S-balanced configurations, containing central ones, which yield simple solutions of the n-body problem. Starting from recent results of the first and third authors, we study the existence of continua of bifurcations branching from a trivial branch of collinear S-balanced configurations and provide an estimate from below on the number of bifurcation instants. In the last part of the paper, by using the continuation method, we explicitly display the bifurcation branches in the case of the three body problem for different choices of the masses.