Related papers: Instabilities and chaos in the classical three-bod…
In this paper we study the linear stability of relative equilibria in the Newtonian $n$-body problem from the viewpoint of electromagnetic systems. We first examine the effect of the ambient dimension on stability, starting from the…
Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical…
In Papers I and II, we have used a free-energy minimization approach that stems from the Landau-Ginzburg theory of phase transitions to describe in simple and clear physical terms the secular and dynamical instabilities as well as the…
We present a numerical study on the stability of all fourth- and fifth-order retrograde mean motion resonances (1/3, 3/1, 1/4, 4/1, 2/3, and 3/2) in the 3-body problem composed of a solar mass star, a Jupiter mass planet, and an additional…
We present a numerical study on the stability of the 1/2, 2/1 and 1/1 retrograde mean motion resonances in the 3-body problem composed of a solar mass star, a Jupiter mass planet and an additional body with zero mass (elliptic restricted…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
A system of $N$ rotators is investigated with a constraint given by a condition of vanishing sum of the cosines of the rotation angles. Equations of the dynamics are formulated and results of numerical simulation for the cases $N$=3, 4, and…
Recent numerical results seem to suggest that in certain regimes of typical particle velocities the gravitational $N-$body problem (for $3\leq N\lesssim 10^3$) is intrinsically less chaotic when the post-Newtonian (PN) force terms are…
We have investigated the appearance of chaos in the 1-dimensional Newtonian gravitational three-body system (three masses on a line with $-1/r$ pairwise potential). We have concentrated in particular on how the behavior changes when the…
The restricted planar elliptic three body problem (RPETBP) describes the motion of a massless particle (a comet) under the gravitational field of two massive bodies (the primaries, say the Sun and Jupiter) revolving around their center of…
We study a particular kind of chaotic dynamics for the planar 3-centre problem on small negative energy level sets. We know that chaotic motions exist, if we make the assumption that one of the centres is far away from the other two (see…
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…
The now-famous Majumdar-Papapetrou exact solution of the Einstein-Maxwell equations describes, in general, $N$ static, maximally charged black holes balanced under mutual gravitational and electrostatic interaction. When $N=2$, this…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…
In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "Euler Integral", is a quasi-integral along the trajectories…
The description of unstable motions in the Restricted Planar Circular 3-Body Problem, modeling the dynamics of a Sun-Planet-Asteriod system, is one of the fundamental problems in Celestial Mechanics. The goal of this paper is to analyze…
We investigate the equal-mass 3-body system in general relativistic lineal gravity in the presence of a cosmological constant $\Lambda$. The cosmological vacuum energy introduces features that do not have a non-relativistic counterpart,…
In this work, we investigate the Earth-Moon system, as modeled by the planar circular restricted three-body problem, and relate its dynamical properties to the underlying structure associated with specific invariant manifolds. We consider a…
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…