Related papers: Relative equilibria in continuous stellar dynamics
Relativistic rotation is considered in the limit of angular velocity approaching zero and radial distance approaching infinity, such that centrifugal acceleration is immeasurably small while tangent velocity remains close to the speed of…
Using the properties of the angular momentum, we develop a new geometrical technique to study relative equilibria for a system of $3$--bodies with positive masses, moving on the two sphere under the influence of an attractive potential…
Much of standard galaxy dynamics rests on the implicit assumption that the corresponding N-body problem is (near) integrable. This notion although leading to great simplification is by no means a fact. It is therefore important to develop…
We develop a model for spiral galaxies based on a nonlinear realization of the Newtonian dynamics starting from the momentum and mass conservations in the phase space. The radial solution exhibits a rotation curve in qualitative accordance…
Stellar pulsations in rotating relativistic stars are reviewed. Slow rotation approximation is applied to solving the Einstein equations. The rotational effects on the non-axisymmetric oscillations are explicitly shown in the polar and…
In this paper we consider a Vlasov or collisionless Boltzmann equation describing the dynamics of planetary rings. We propose a simple physical model, where the particles of the rings move under the gravitational Newtonian potential of two…
In this paper we classify the free boundary associated to equilibrium configurations of compressible, self-gravitating fluid masses, rotating with constant angular velocity. The equilibrium configurations are all critical points of an…
In this article, equilibrium points and families of periodic orbits in the vicinity of the collinear equilibrium points of a binary asteroid system are investigated with respect to the angular velocity of the secondary body, the mass ratio…
In order to simulate rigidly rotating polytropes we have simulated systems of $N$ point particles, with $N$ up to 1800. Two particles at a distance $r$ interact by an attractive potential $-1/r$ and a repulsive potential $1/r^2$. The…
Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
In this paper, we present a "stellar dynamics" model of an infinite Universe, where matter distribution follows an inverse proportionality squared relationship with respect to the distance from the rotation center of galaxy clusters and…
This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information one could obtain about the equation of state of matter at extremely high densities and because…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
This paper considers the stability of tidal equilibria for planetary systems in which stellar rotation provides a significant contribution to the angular momentum budget. We begin by applying classic stability considerations for two bodies…
We present solutions to the Einstein-Klein Gordon system representing boson stars in the slow rotation approximation. By considering slow rotation we are able to reduce the number of equations yielding a system of ordinary differential…
We prove existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler-Poisson (EP) equations in 3 spatial dimensions, with prescribed angular momentum and total mass. This problem can be…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…