Related papers: Stable Orbits of Rigid, Rotating, Precessing, Mass…
Stability of supermassive stars embedded in hot dark matter is investigated on the base of the energetic method. Stability effect of dark mater is compared with rotational stabilization and preference of the last factor is advocated.
This paper is devoted to Radial Orbit Instability in the context of self-gravitating dynamical systems. We present this instability in the new frame of Dissipation-Induced Instability theory. This allows us to obtain a rather simple proof…
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…
We give a self-contained modern linear stability analysis of a system of n equal mass bodies in circular orbit about a single more massive body. Starting with the mathematical description of the dynamics of the system, we form the linear…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
Path equations of different orbiting objects in the presence of very strong gravitational fields are essential to examine the impact of its gravitational effect on the stability of each system. Implementing an analogous method, used to…
A single frictional elastic disk, supported against gravity by two others, rotates steadily when the supports are vibrated and the system is tilted with respect to gravity. Rotation is here studied using Molecular Dynamics Simulations, and…
Recent work on the equilibrium and stability of ellipsoidal stellar systems is reviewed. The absence of constant-density cores in early-type galaxies implies that chaos and high-order resonances are generic features of the motion in…
We study well-posedness, stabilization and control problems involving freely vibrating beams that may undergo motions of large magnitude -- i.e. large displacements of the reference line and large rotations of the cross sections. Such…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…
For the closed string carrying 2 or 3 point-like masses the stability problem for central and linear rotational states is considered. This problem is important for applications of these model to describing baryons, glueballs or other exotic…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
As a direct result of ongoing efforts to detect more exoplanetary systems, an ever-increasing number of multiple-planet systems are being announced. But how many of these systems are truly what they seem? In many cases, such systems are…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are…
The dynamical stability of cosmic rings, or vortons, is investigated for the particular equation of state given by the Witten bosonic model. It is found that there exists a finite range of the state parameter for which the vorton states are…
We study analytically and numerically the stability of the pressure-less, viscously spreading accretion ring. We show that the ring is unstable to small non-axisymmetric perturbations. To perform the perturbation analysis of the ring we use…