Related papers: Kepler orbits of settling discs

We derive the kinetic equation that describes the secular evolution of a large set of particles orbiting a dominant massive object, such as stars bound to a supermassive black hole or a proto-planetary debris disc encircling a star. Because…

We develop a theoretical framework and use two-dimensional hydrodynamical simulations to study the repulsive effect between two close orbiters embedded in an accretion disk. We consider orbiters on fixed Keplerian orbits with masses low…

In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…

Exact results for three trajectories of small numbers of particles interacting hydrodynamically through Stokeslets are presented. First, the middle particle in a vertical trio of particles sediments at a constant velocity for all time.…

We report on the emergence of spontaneously rotating clusters in active emulsions. Ensembles of self-propelling droplets sediment and then self-organise into planar, hexagonally ordered clusters which hover over the container bottom while…

We analytically work out the long-term, i.e. averaged over one orbital revolution, time variations of some direct observable quantities Y induced by classical and general relativistic dynamical perturbations of the two-body pointlike…

We describe the dynamics and thermodynamics of collisionless particle disks orbiting a massive central body, in the case where the disk mass is small compared to the central mass, the self-gravity of the disk dominates the non-Keplerian…

Stellar multiple systems play a pivotal role in cluster dynamics and stellar evolution, leading to intense astronomical phenomena like X-ray binaries, gamma-ray bursts, Type Ia supernova, and stellar mergers, which are prime sources of…

We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…

The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…

We carry out a general study of the stability of astrophysical flows that appear steady in a uniformly rotating frame. Such a flow might correspond to a stellar pulsation mode or an accretion disk with a free global distortion giving it…

The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an…

We examine the formation of planets around binary stars in light of the recently discovered systems Kepler 16, 34 and 35. We conduct hydrodynamical simulations of self gravitating disks around binary systems. The selected binary and disk…

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms…

A new description of the dynamics of warped accretion discs is presented. A theory of fully nonlinear, slowly varying bending waves is developed, involving a proper treatment of viscous fluid dynamics but neglecting self-gravitation. The…

Studying the orbital stability of multi-planet systems is essential to understand planet formation, estimate the stable time of an observed planetary system, and advance population synthesis models. Although previous studies have primarily…

We use Hamiltonian Floer theory to recover and generalize a classic rigidity theorem of Ekelend and Lasry. That theorem can be rephrased as an assertion about the existence of multiple closed Reeb orbits for certain tight contact forms on…

We give some results about the dynamics of a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. Our main results concern (1) singularities and (2) the dynamics in…

The Earth itself is not stationary but keeps revolving, and its motion further satisfies the law of equal area according to the heliocentric doctrine. That satisfaction can be used to construct the mathematical relationships between the…

We present here a simple hydrodynamic model based on a sequence of steady states of the inner sub-Keplerian accretion disc to model its spectral states. Correlations between different hydrodynamic steady states are studied with a goal to…