相关论文: Bifurcation and stability of uniformly rotating ho…
The equilibrium of incompressible spheroid-ring systems in rigid rotation is investigated by numerical means for a unity density contrast. A great diversity of binary configurations is obtained, with no limit neither in the mass ratio, nor…
A rotating system, such as a star, liquid drop, or atomic nucleus, may rotate as an oblate spheroid about its symmetry axis or, if the angular velocity is greater than a critical value, as a triaxial ellipsoid about a principal axis. The…
We consider the gravitational potential of a rotating star with non-uniform density to derive the orbital and epicyclic frequencies of the particles orbiting the star. We assume that the star is composed of concentric spheroids of constant…
We derive an analytical trace formula for the level density of the two-dimensional elliptic billiard using an improved stationary phase method. The result is a continuous function of the deformation parameter (eccentricity) through all…
This paper is concerned with the problem of an ellipsoid of revolution rolling on a horizontal plane under the assumption that there is no slipping at the point of contact and no spinning about the vertical. A reduction of the equations of…
We show that a rigidly rotating, homogeneous ellipsoid of revolution threaded by a uniform, coaxial magnetic field is a possible figure of equilibrium. While the spheroidal shape is fully preserved, the rotation rate is modified.…
With regard to homeoidally striated Jacobi ellipsoids, a unified theory of systematically rotating and peculiar motions is developed, where both real and imaginary rotation are considered. The effect of positive or negative residual motion…
We give a thorough investigation of sequences of uniformly rotating, homogeneous axisymmetric Newtonian equilibrium configurations that bifurcate from highly flattened Maclaurin spheroids. Each one of these sequences possesses a…
We investigate the effects of extended mass and spheroidal deformation on the periapsis shift of quasi-circular orbits inside a gravitating mass distribution in the Newtonian framework. The analysis is restricted to orbits confined to the…
Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode perturbations when viscosity is present. The intuitive explanation is that energy…
Elliptical galaxies are modelled as homeoidally striated Jacobi ellipsoids where the peculiar velocity distribution is anisotropic, or equivalently as their adjoints configurations i.e. classical Jacobi ellipsoids of equal mass and axes, in…
The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the…
The boundaries of the Uranian epsilon, alpha, and beta rings can be fitted by Keplerian ellipses. The pair of ellipses that outline a given ring share a common line of apsides. Apse alignment is surprising because the quadrupole moment of…
This paper studies a class of $1\frac12$-degree-of-freedom Hamiltonian systems with a slowly varying phase that unfolds a Hamiltonian pitchfork bifurcation. The main result of the paper is that there exists an order of…
We derive an effective equation of motion for the orientational dynamics of a neutrally buoyant spheroid suspended in a simple shear flow, valid for arbitrary particle aspect ratios and to linear order in the shear Reynolds number. We show…
The self-similar equilibrium models of self-gravitating, rotating, isothermal systems are investigated analytically. In these models the rotation velocity is constant and the density varies as $\frac{f(\theta, \phi)}{r^2}$, where $r$ and…
We report on transcritical bifurcations of periodic orbits in non-integrable two-dimensional Hamiltonian systems. We discuss their existence criteria and some of their properties using a recent mathematical description of transcritical…
Ordinary differential equations describing the self-similar collapse of a rotating, magnetized, self-gravitating and isothermal filament are derived. Explicit homologous solutions are studied with special emphasis on the bifurcation that…
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…