相关论文: Stability of Triangular Equilibrium Points in Robe…

We present a purely theoretical study of the morphological evolution of self-gravitating systems formed through the dissipationless collapse of N-point sources. We explore the effects of resolution in mass and length on the growth of…

We consider the two-body problem on surfaces of constant non-zero curvature and classify the relative equilibria and their stability. On the hyperbolic plane, for each q>0 we show there are two relative equilibria where the masses are…

Continuing work initiated in an earlier publication [Ichita, Yamada and Asada, Phys. Rev. D 83, 084026 (2011)], we reexamine the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three…

We conducted extensive numerical experiments of equal mass three-body systems until they became disrupted. The system lifetimes, as a bound triple, and the Lyapunov times show a correlation similarto what has been earlier obtained for small…

In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…

The stability issue of a large class of modified gravitational models is discussed with particular emphasis to de Sitter solutions. Three approaches are briefly presented and the generalization to more general cases is mentioned.

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…

We study relative equilibria ($RE$ in short) for three-body problem on $\mathbb{S}^2$, under the influence of a general potential which only depends on $\cos\sigma_{ij}$ where $\sigma_{ij}$ are the mutual angles among the masses. Explicit…

The set of volumes of stable surfaces does have accumulation points. In this paper, we study this phenomenon for surfaces with one cyclic quotient singularity, towards answering the question under which conditions we can still have…

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…

The planar linear restricted four-body problem is used in order to determine the Newton-Raphson basins of convergence associated with the equilibrium points. The parametric variation of the position as well as of the stability of the…

Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive…

In the paper a solution for equilibrium configurations of an elastic beam subject to three points bending is given in terms of Jacobi elliptical functions. General equations are derived and the domain of solution is established. Several…

We establish the well-posedness of a coupled micro-macro parabolic-elliptic system modeling the interplay between two pressures in a gas-liquid mixture close to equilibrium that is filling a porous media with distributed microstructures.…

We prove for generalisations of quasi-homogeneous $n$-body problems with center of mass zero and $n$-body problems in spaces of negative constant Gaussian curvature that if the masses and rotation are fixed, there exists, for every order of…

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under…

We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the…

It is well known that, from the Newtonian point of view, the Lagrangian point $L_4$ in the circular restricted three body is stable if $\mu< \frac{1}{18}(9-\sqrt{19})\approx 0.03852$. In this paper we will provide a formula that allows us…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

The three-body general problem is formulated as a problem of geodesic trajectories flows on the Riemannian manifold. It is proved that a curved space with local coordinate system allows to detect new hidden symmetries of the internal motion…