Related papers: Stable Orbits of Rigid, Rotating, Precessing, Mass…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
We present the first concrete evidence for the classical stability of vortons, circular cosmic string loops stabilized by the angular momentum of the charge and current trapped on the string. We begin by summarizing what is known about…
This note adds some critical remarks on the discussion presented in the McDonald's paper ([1]) on stability of steady motion of the well known problem of a disk rolling on a rough horizontal plane.
This work investigates experimentally and numerically the dynamics of rigid particles settling under gravity in a highly viscous fluid. We demonstrate that certain shapes: cones, crescent moons, arrowheads, and open flat rings reorient and…
Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique…
We study the evolution of magnetized and rigidly rotating neutron stars within a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions. The stars are modeled as…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical…
We show the existence of stable bound orbits for the massive and massless particles moving in the simplest microstate geometry spacetime in the bosonic sector of the five-dimensional minimal supergravity. In our analysis, reducing the…
The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience…
We built two self-consistent models of triaxial, cuspy, rotating stellar systems adding rotation to non-rotating models presented in previous papers of this series. The final angular velocity of the material is not constant and varies with…
In his 1856 Adams Prize essay, James Clark Maxwell demonstrated that Saturn's rings cannot be comprised of a uniform rigid body. This is a consequence of the two-body gravitational interaction between a ring and planet resulting in…
The radial-orbit instability is a collective phenomenon that has heretofore only been observed in spherical systems. We find that this instability occurs also in triaxial systems, as we checked by performing extensive N-body simulations…
We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear beam…
Ring galaxies are amazing objects exemplified by the famous case of the Hoag's Object. Here the mass of the central galaxy may be comparable to the mass of the ring, making it a difficult case to model mechanically. In a previous paper, it…
Locating the position of periodic orbits in galaxies is undoubtedly an issue of paramount importance. We reveal the position and the stability of periodic orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric…
The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters,…
Exoplanet detection surveys revealed the existence of numerous multi-planetary systems packed close to their stability limit. In this proceeding, we review the mechanism driving the instability of compact systems, originally published in…
It is well established that certain detached eclipsing binary stars exhibit apsidal motions whose value is in disagreement with with calculated deviations from Keplerian motion based on tidal effects and the general theory of relativity.…