Related papers: Stability, periodic orbits and KAM tori in the dyn…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
The Stark problem is Kepler problem with an external constant acceleration. In this paper, we study the periodic orbits for Stark problem for both planar case and spatial case. We have conducted a detailed analysis of the invariant tori and…
We consider the special case of the restricted circular three-body problem, when the two primaries are of equal mass, while the third body of negligible mass performs oscillations along a straight line perpendicular to the plane of the…
We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of…
The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…
In this paper, we consider a time-periodically forced Kepler problem in any dimensions, with an external force which we only assume to be regular in a neighborhood of the attractive center. We prove that there exist infinitely many periodic…
We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by using the orbital moment and its time derivative. We show that it is possible to get some insight into the stability…
In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic…
In this paper we discuss about the possibility of {\it coexistence} of stable and unstable quasi--periodic {\sc kam} tori in a region of phase space of the three-body problem. The {argument of proof} goes along {{\sc kam} theory and,…
We study in detail the motions of three planets interacting with each other under the influence of a central star. It is known that the system with more than two planets becomes unstable after remaining quasi-stable for long times, leading…
In this paper, we use the restricted three body problem in the binary stellar systems, taking photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the…
We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.
The orbits about Lagrangian equilibrium points are important for scientific investigations. Since, a number of space missions have been completed and some are being proposed by various space agencies. In light of this, we consider a more…
The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is…
We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating…
Based on quantitative ``{\sc kam} theory'', we state and prove two theorems about the continuation of maximal and whiskered quasi--periodic motions to slightly perturbed systems exhibiting proper degeneracy. Next, we apply such results to…
The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is…
We study the planetary system of $\upsilon$~Andromed{\ae}, considering the three-body problem formed by the central star and the two largest planets, $\upsilon$~And~\emph{c} and $\upsilon$~And~\emph{d}. We adopt a secular, three-dimensional…
We consider a curved Sitnikov problem, in which an infinitesimal particle moves on a circle under the gravitational influence of two equal masses in Keplerian motion within a plane perpendicular to that circle. There are two equilibrium…