Related papers: Three-body problem -- from Newton to supercomputer…
The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…
Astrophysical Challenges which demand the solution of the one million (or more) gravitating body problem are briefly discussed for the fields of cosmology, galactic nuclei and globular star clusters. Results from the classical three-body…
Since Poincar\'e, periodic orbits have been one of the most important objects in dynamical systems. However, searching them is in general quite difficult. A common way to find them is to construct families of periodic orbits which start at…
Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton's method based on the continuous analog of Newton's method and a high precision arithmetic for a specialized…
Using the variational method, Chenciner and Montgomery (2000 Ann. Math. 152 881--901) proved the existence of an eight-shaped periodic solution of the planar three-body problem with equal masses. Just after the discovery, Gerver have…
There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to…
Chaotic systems such as the gravitational N-body problem are ubiquitous in astronomy. Machine learning (ML) is increasingly deployed to predict the evolution of such systems, e.g. with the goal of speeding up simulations. Strategies such as…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
Long-period circumbinary planets appear to be as common as those orbiting single stars and have been found to frequently have orbital radii just beyond the critical distance for dynamical stability. Assessing the stability is typically done…
The three-body problem is arguably the oldest open question in astrophysics, and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but…
We review some recent progress on the research of the periodic orbits of the N-body problem,and propose a numerical scheme to determine the spatial doubly-symmetric periodic orbits (SDSPs for short). Both comet- and lunar-type SDSPs in the…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
We develop a new method for solving two- and three-body bound state problems using unsupervised machine learning techniques. We use a deep neural network to calculate both simple and realistic potentials, obtaining the properties of the…
A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on…
A state-of-the-art method that combines a quantum computational algorithm and machine learning, so-called quantum machine learning, can be a powerful approach for solving quantum many-body problems. However, the research scope in the field…
We design an accurate orbital integration scheme for the general N-body problem preserving all the conserved quantities but the angular momentum.This scheme is based on the chain concept (Mikkola & Aarseth 1993) and is regarded as an…
Recovering trajectories of quantum systems whose classical counterparts display chaotic behavior has been a subject that has received a lot of interest over the last decade. However, most of these studies have focused on driven and…
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and its many different families of unstable periodic orbits…