相关论文: Circular orbits of a ball on a rotating conical tu…

Numerical solutions are presented for a family of finite angular momentum orbits with three equal masses which connects the classical circular Lagrange orbit with the recently discovered planar figure eight orbit. Each member of this family…

Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…

We consider the motion of a particle subjected to the constant gravitational field and scattered inelasticaly by hard boundaries which possess the shape of parabola, wedge, and hyperbola. The billiard itself performs oscillations. The…

We report experimental measurements of the translational and rotational dynamics of a large buoyant sphere in isotropic turbulence. We introduce an efficient method to simultaneously determine the position and (absolute) orientation of a…

The main aim of this work was to give constructive proof of stable orbital motions existence in the systems of bodies, which interact only by magnetic forces.

An iterative method is presented for solving the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity by expanding about the thin ring limit. Using this method, a simple formula relating mass to…

The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…

The controlled motion of a rolling ball actuated by internal point masses that move along arbitrarily-shaped rails fixed within the ball is considered. The controlled equations of motion are solved numerically using a predictor-corrector…

We study a viable connection between the circular-equatorial orbits and reflection symmetry across the equatorial plane of a vacuum stationary axis-symmetric spacetime in general relativity. The behavior of the circular equatorial orbits in…

In this paper, we present a rotating de Rham-Gabadadze-Tolley black hole with a positive cosmological constant in massive gravity, achieved by applying a modified Newman-Janis algorithm. The black hole exhibits stable orbits of constant…

The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…

We consider a strictly convex billiard table with $C^2$ boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation…

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…

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…

The motion of spinning particles around compact objects, for example a rotating stellar object moving around a supermassive black hole, is described by differential equations that are, in general, non-integrable. In this work, we present a…

In this paper we show that, under certain generic conditions, billiards on ovals have only a finite number of periodic orbits, for each period, all non-degenerate and at least one of them is hyperbolic. Moreover, the invariant curves of two…

We study the continuation of periodic orbits from various compound of homoclinics in classical system. Together with the homoclinics, the periodic orbits make up a $C^1$-smooth, normally hyperbolic invariant cylinder with holes. It plays a…

A ``Wick rotation'' is applied to the noncommutative sphere to produce a noncommutative version of the hyperboloids. A harmonic basis of the associated algebra is given. It is noted that, for the one sheeted hyperboloid, the vector space…

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to…

The statistical mechanics of a linear non-interacting polymer chain with a large number of monomers is considered with fixed angular momentum. The radius of gyration for a linear polymer is derived exactly by functional integration. This…