Related papers: Sphere rolling on the surface of a cone
From the simple Lagrangian the equations of motion for the particle with spin are derived. The spin is shown to be conserved on the particle world-line. In the absence of a spin the equation coincides with that of a geodesic. The equations…
The two equations of motion for a test particle are compared with each other. One is in the Non commutative space involving a static rigid sphere (as a source of central force) and the other is in the usual space involving a slowly…
Spiral waves in active media react to small perturbations as particle-like objects. Here we apply the asymptotic theory to the interaction of spiral waves with a localized inhomogeneity, which leads to a novel prediction: drift of the…
In this paper, we consider the dynamics of a heavy homogeneous ball moving under the influence of dry friction on a fixed horizontal plane. We assume the ball to slide without rolling. We demonstrate that the plane may be divided into two…
We report on the controlled transport of drops of magnetic liquid, which are swimming on top of a non-magnetic liquid layer. A magnetic field which is rotating in a vertical plane creates a torque on the drop. Due to surface stresses within…
Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…
It is proved that, according to Classical Mechanics and Electrodynamics, the trajectory of the center of mass of a neutral system of electrical charges can be deflected by an inhomogeneous magnetic field, even if its internal angular…
It is shown that time-harmonic motions of spherical and toroidal surfaces can be deformed non-locally without loosing the existence of infinitely many constants of the motion.
The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters,…
The dynamics of a hollow cylinder containing granules and rolling down an inclined plane was investigated. A theoretical approach for investigating the behaviour of such a cylinder was proposed. The critical angle of the plane that allows…
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.
We explicitly find an exact spherically symmetric solution in quadratic non-metricity gravity. We show that the quadratic term acts as a cosmological constant. This solution contradicts all the claims in the literature that there is no…
We exhibit orbits of the geodesic flow on a hyperbolic surface with at least one cusp such that every tubular neighborhood contains uncountably many distinct geodesic flow orbits. The proof relies on new phenomena, namely the existence of…
A skier's motion was analyzed by a simple model consist of point mass $m$ and a single rod connected to a single ski plate. We studied the conditions for the stable ski turn as functions of the linear velocity and the radius of the turn.…
We investigate self-gravitating rotating solutions in the Einstein-Skyrme theory. These solutions are globally regular and asymptotically flat. We present a new kind of solutions with zero baryon number, which possess neither a flat limit…
The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy,…
This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be…
We find a class of twisted and differentially rotating neutron star magnetospheres that do not have a light cylinder, generate no wind and thus do not spin-down. The magnetosphere is composed of embedded differentially rotating flux…
We study homogeneous cosmological models featuring shift-symmetric scalar fields (or, superfluids) in relative motion. In the presence of anisotropy this universe generally features rotation, in the sense that the principal axes of…
We review a number of results recently obtained in the area of constructing rotating solitons in a four dimensional asymptotically flat spacetime. Various models are examined, special attention being paid to the monopole-antimonopole and…