Related papers: A trial symbolic dynamics of the planar three-body…
Let a number, N, of particles interact classically through Newton's Laws of Motion and Newton's inverse square Law of Gravitation. The resulting equations of motion provide an approximate mathematical model with numerous applications in…
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…
Despite the huge number of research into the three-body problem in physics and mathematics, the study of this problem still remains relevant both from the point of view of its broad application and taking into account its fundamental…
This survey paper is aimed to describe a relatively new branch of symbolic dynamics which we call Arithmetic Dynamics. It deals with explicit arithmetic expansions of reals and vectors that have a "dynamical" sense. This means precisely…
In active matter and living matter, such as clusters of migrating cells, collective dynamics emerges from the underlying interactions. A common assumption of theoretical descriptions of collective cell migration is that these interactions…
The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), of which the motion gives us general solutions of the three body problem. A…
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…
The introduction of optical tweezers for trapping atoms has opened remarkable opportunities for manipulating few-body systems. Here, we present the first bottom-up assembly of atom triads. We directly observe atom loss through inelastic…
We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy ``piston'', with elastic collisions between particles but inelastic collisions between the light particles and the interval…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
We discuss the general three-particle quantum scattering problem, for motion restricted to the full line. Specifically, we formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As a…
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…
Geometrical properties of three-body orbits with zero angular momentum are investigated. If the moment of inertia is also constant along the orbit, the triangle whose vertexes are the positions of the bodies, and the triangle whose…
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…
The gravitational three-body problem is a rich open problem, dating back to Newton. It serves as a prototypical example of a chaotic system and has numerous applications in astrophysics. Generically, the motion is non-integrable and…
Without involving bounce events, a Poincar\'e section associated with the axes is found to give a map on the annulus for the diamagnetic Kepler problem. Symbolic dynamics is then established based on the lift of the annulus map. The…
Expressing physics problems in the form of a mathematical model is one of the most important stages in the problem-solving process. Particularly in algebraic symbolization, understanding the meanings of signs and being able to manipulate…
In a fast scrambling many-body quantum system, information is spread and entanglement is built up on a timescale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body…
The dynamics of the Restricted 3 Body Problem in the Post Newtonian context have been, and continue to be, studied extensively and a number of characteristics such as ejections of bodies from the system, precession of orbits, chaotic…
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…