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

Phenomena of rotation and oscillations of particle spin are discussed for particles rotating in storage ring. The fact that these effects are described by spin-dependent part of zero-angle scattering amplitude allows to use them for the…

We consider the mechanical equilibrium and stability of matter trapped in the magnetosphere of a rapidly rotating star. Assuming a dipolar magnetic field and arbitrary inclination of the magnetic axis with respect to the axis of rotation we…

In this paper, we study rotation numbers of random dynamical systems on the circle. We prove the existence of rotation numbers and the continuous dependence of rotation numbers on the systems. As an application, we prove a theorem on…

When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order…

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth…

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous…

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…

We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary, and also a circular scatterer in the interior of the disk. We investigate stability properties of some…

We study motion of charged particles in the field of a rotating black hole immersed into an external asymptotically uniform magnetic field, focusing on the epicyclic quasi-circular orbits near the equatorial plane. Separating the circular…

The dynamics of three soft interacting particles on a ring is shown to correspond to the motion of one particle inside a soft triangular billiard. The dynamics inside the soft billiard depends only on the {\it masses ratio} between…

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described…

Problems involving rotating systems analyzed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. One of the problems that I…

In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is…

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on…

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being…

We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…

We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is always circular, and determined by a simple relation between…

We report a novel and spectacular instability of a fluid surface in a rotating system. In a flow driven by rotating the bottom plate of a partially filled, stationary cylindrical container, the shape of the free surface can spontaneously…

The motion of a satellite around a planet can be studied by the Hill model, which is a modification of the restricted three body problem pertaining to motion of a satellite around a planet. Although the dynamics of the circular Hill model…