Related papers: An explicit solution to the spinning ring problem

The physical properties of an axisymmetric black-hole-ring system are studied analytically within the framework of general relativity to second order in the dimensionless mass ratio $\mu\equiv m/M$. In particular, we analyze the asymptotic…

We analyze stability of a thin inextensible elastic rod which has non-vanishing spontaneous generalized torsions in its stress-free state. Two classical problems are studied, both involving spontaneously twisted rods: a rectilinear beam…

Spin relaxation dynamics in rings with Rashba spin-orbit coupling is investigated using spin kinetic equation. We find that the spin relaxation in rings occurs toward a persistent spin configuration whose final shape depends on the initial…

The spin-dynamics of two alkali atoms in an optical tweezer is driven by spin-changing collisions that couple the spin-state of the atoms to their relative motion. This paper experimentally studies the resulting spin-states when the…

Humanoid robots locomote by making and breaking contacts with their environment. A crucial problem is therefore to find precise criteria for a given contact to remain stable or to break. For rigid surface contacts, the most general…

We consider a nonlinear model equation describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. In the present problem setting, we also take into account the effect of external flow. We prove the unique…

Steady, dihedrally symmetric patterns with sharp peaks may be observed on a spinning skirt, lagging behind the material flow of the fabric. These qualitative features are captured with a minimal model of traveling waves on an inextensible,…

This work presents a study on the nonrelativistic quantum motion of a charged particle in a rotating frame, considering the Aharonov-Bohm effect and a uniform magnetic field. We derive the equation of motion and the corresponding radial…

We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We…

We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a…

We study the dynamics of pure phase decoherence for a particle hopping around an N-site ring, coupled both to a spin bath and to an Aharonov-Bohm flux which threads the ring. Analytic results are found for the dynamics of the influence…

An exact rotating anisotropic fluid solution and a family of exact rotating anisotropic fluid solutions are presented which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor the…

We apply two theoretical and two numerical methods to the problem of a disk placed in a groove and subjected to gravity and a torque. Methods assuming rigid particles are indeterminate -- certain combinations of forces cannot be calculated,…

Euler's rotation theorem states that any reconfiguration of a rigid body with one of its points fixed is equivalent to a single rotation about an axis passing through the fixed point. The theorem forms the basis for Chasles' theorem which…

Contraction analysis uses a local criterion to prove the long-term behaviour of a dynamical system. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions contracts. If adjacent solutions…

We study inertial motions of the coupled system, S, constituted by a rigid body containing a cavity that is completely filled with a viscous liquid. We show that for data of arbitrary size (initial kinetic energy and total angular momentum)…

The control problem of the working tool movement along a predefined trajectory is considered. The integral of kinetic energy and weighted inertia forces for the whole period of motion is considered as a cost functional. The trajectory is…

We examine some debated points in current discussions about rotating stars: the shape, the gravity darkening, the critical velocities, the mass loss rates, the hydrodynamical instabilities, the internal mixing and N--enrichments. The study…

A net circulating current may appear within a quantum ring under finite bias. We study the characteristic features of the circular current in the presence of Rashba spin-orbit interaction (RSOI). Both charge and spin currents appear within…

The dynamics of a set of identical spins interacting with another one through a time-dependent coupling gives rise to a gyroscopic equation with a variable Larmor frequency and, more importantly, with an operator playing the role a Larmor…