Related papers: Generalized three body problem and the instability…
In the core accretion model for the formation of gas giant planets, runaway gas accretion onto a core is the primary requisite, triggered when the core mass reaches a critical value. The recently revealed wide diversity of the extrasolar…
The stellar ejection rate and the rates of change of the binary semimajor axis and eccentricity are derived from scattering experiments for the restricted three-body problem. They are used to study the evolution of binaries in simple models…
The discovery of Pluto's small moons in the last decade brought attention to the dynamics of the dwarf planet's satellites. With such systems in mind, we study a planar $N$-body system in which all the bodies are point masses, except for a…
The three-body problem has been studied for more than three centuries [1,2], and has received much attention in recent years [3-5]. It shows complex dynamical phenomena due to the mutual gravitational interaction of the three bodies. Triple…
Numerous previous studies have investigated the phenomenon wherein initially spherical N-body systems are distorted to triaxial shapes. We report on an investigation of a previously described orbital instability that should oppose…
With the help of 3D MHD simulations we investigate the collapse and fragmentation of rotating turbulent prestellar core embedded into turbulent medium. The numerical code is based on a high resolution Godunov-type finite-difference scheme.…
Very massive stars are thought to be formed in the early Universe because of a lack of cooling process by heavy elements, and might have been responsible for the later evolution of the Universe. We had an interest in vibrational stability…
We perform a non-radial adiabatic perturbation analysis on homologous conventional polytropic stellar core collapses. The core collapse features a polytropic exponent $\Gamma=4/3$ relativistic gas under self-gravity of spherical symmetry…
The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that all three bodies…
We construct a Nekhoroshev-like result of stability with sharp constants for the planar three body problem, both in the planetary and in the restricted circular case, by using the periodic averaging technique. Our constructions can be…
Lunar mean-motion resonances (MMRs) significantly shape cislunar dynamics beyond GEO, forming stable-unstable orbit pairs with corresponding intermingled chaotic and regular regions. The resonance zone is rigorously defined using the…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
This thesis studies instabilities and singularities in a geometrical approach to the planar 3-body problem as well as instabilities, chaos and ergodicity in the 3-rotor problem. Trajectories of the planar 3-body problem are expressed as…
We study the stability of trajectories near the disk plane of galaxy models with a triaxial dark matter halo component. We also examine the effect of weak discreteness noise, rapidly rotating bar perturbations and weak dissipation on these…
The Sitnikov problem is a special case of the restricted three-body problem where the primaries moves in elliptic orbits of the two-body problem with eccentricity $e\in [0,1[$ and the massless body moves on a straight line perpendicular to…
The near-horizon geometries of the spinning D3-, M2- and M5-branes are examined by the probes immersed in a co-rotating frame. It is found that the geometries become unstable at critical values of the spin angular velocity by emitting the…
Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd…
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…
In this paper, we present preliminary results on the stability of massless particles in two and three-planet systems. The results of our study may be used to address questions concerning the stability of terrestrial planets in these systems…
Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel…