Related papers: An explicit solution to the spinning ring problem
The exact equation of spin motion in a cylindrical coordinate system with allowance for electric dipole moments of particles has been derived. This equation is convenient for analytical calculations of spin dynamics in circular storage…
The surface rotations of some red giants are so fast that they must have been spun up by tidal interaction with a close companion, either another star, a brown dwarf, or a planet. We focus here on the case of red giants that are spun up by…
A long standing conjecture in Hamiltonian Dynamics states that every contact form on the standard contact sphere $S^{2n+1}$ has at least $n+1$ simple periodic Reeb orbits. In this work, we consider a refinement of this problem when the…
We consider a disk-shaped thin elastic sheet bonded to a compliant sphere. (Our sheet can slip along the sphere; the bonding controls only its normal displacement.) If the bonding is stiff (but not too stiff), the geometry of the sphere…
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…
Usual explanations of spiral galaxy rotation curves assume circular orbits of stars. The consequences of giving up this assumption are investigated here. In particular, hyperbolic stellar trajectories are found to be interesting. The two…
The article discusses the steady motion of a rigid disk of finite thickness rolling on its edge on a horizontal plane under the influence of gravity. The governing equations are presented and two cases allowing for a steady state solution…
Spin textures of one or two electrons in a quantum dot with Rashba or Dresselhaus spin-orbit couplings reveal several intriguing properties. We show that even at the single-electron level spin vortices with different topological charges…
We show that the friction force and torque, acting at a dry contact of two objects moving and rotating relative to each other, are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is…
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…
A rotating stationary solution of the vacuum Einstein equations with a cosmological constant is exhibited which reduces to de Sitter's interior cosmological solution when the angular momentum goes to zero. This solution is locally…
Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are…
Spherical robots typically require at least two actuators to achieve controlled 2D planar motion. Here we present Rollbot, the first spherical robot capable of controllably maneuvering on a 2D plane with a single actuator, challenging this…
The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
Twistors appear to provide a satisfactory treatment of angular momentum for gravitationally radiating systems. The approach is manifestly Bondi-Metzner-Sachs (BMS) invariant, and there are no supertranslation ambiguities. The resulting…
We study Heisenberg model of classical spins lying on the toroidal support, whose internal and external radii are $r$ and $R$, respectively. The isotropic regime is characterized by a fractional soliton solution. Whenever the torus size is…
One of the most challenging problems in polymer physics is providing a theoretical description for the behaviour of rings in dense solutions and melts. Although it is nowadays well established that the overall size of a ring in these…
We present a new exact solution for a general non-BPS black ring in the bosonic sector of five-dimensional minimal supergravity. This obtained solution carries four independent conserved charges: the mass, two angular momenta, an electric…
In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…
We present several new results, extending our recent proposal of a spin filter based on a tight-binding model for a periodic chain of diamond-like loops [Phys. Rev. B {\bf 78}, 125328 (2008)]. In this filter, the Rashba spin-orbit…