Related papers: Relative Equilibria in the Spherical, Finite Densi…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial…
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…
Numerical solutions are presented for a family of finite angular momentum orbits with three equal masses which connects the classical circular Lagrange orbit with the recently discovered planar figure eight orbit. Each member of this family…
We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we…
We consider a continuum of particles that are acted upon by an external force $\mathbf{G}(t,\mathbf{x})$ and that collide with a rigid body. The body itself is subject to a constant force $E$ as well as to the collective force of…
In this paper the non-canonical Hamiltonian dynamics of a gyrostat in the three body problem will be examined. By means of geometric-mechanics methods some relative equilibria of the dynamics of a gyrostat in Newtonian interaction with two…
The static n-body problem of General Relativity states that there are, under a reasonable energy condition, no static $n$-body configurations for $n > 1$, provided the configuration of the bodies satisfies a suitable separation condition.…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
In this paper we investigate gravitationally bound, spherically symmetric equilibrium configurations consisting of ordinary (polytropic) matter nonminimally coupled to an external chameleon scalar field. We show that this system has static,…
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…
We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the…
We interpret the exact solutions previously obtained for spherically symmetric shells of liquid fluid in General Relativity in terms of the energies involved. We show that a certain parameter that was introduced into the solutions by the…
We consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials…
An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…
The classical three-body harmonic system in $\mathbb{R}^d$ ($d>1$) with finite rest lengths and zero total angular momentum $L=0$ is considered. This model describes the dynamics of the $L=0$ near-equilibrium configurations of three point…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by…
Resolution-Scale Relativity suggests quantum-like dynamics may emerge in chaotic macroscopic systems. In planetary systems, this would lead to orbital periods being proportional to cubed integers $n$. Each system is then characterized by a…
All axisymmetric self-similar equilibria of self-gravitating, rotating, isothermal systems are identified by solving the nonlinear Poisson equation analytically. There are two families of equilibria: (1) Cylindrically symmetric solutions in…