相关论文: The rolling sphere and the quantum spin

In this paper we study the orbits of massive bodies moving in the spacetime generated by a spherically symmetric and non-rotating distribution of mass. More specifically, our treatment discusses the more accurate calculation of the…

Suppose that the initial triangle formed by the three moving masses of the three-body problem is similar to the triangle formed at some later time. We derive a simple integral formula for the overall rotation relating the two triangles. The…

We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…

We give a complete answer to the question of when two curves in two different Riemannian manifolds can be seen as trajectories of rolling one manifold on the other without twisting or slipping. We show that up to technical hypotheses, a…

The circular motion of spinning massive test particles in the equatorial plane of a rotating black hole is investigated in the case in which the components of the spin tensor are allowed to vary along the orbit.

We present the N=2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged particle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature…

The problem of a disc or cylinder initially rolling with slipping on a surface and subsequently transitioning to rolling without slipping is often cited in textbooks. The following experiment serves to clearly demonstrate the transition…

This paper is concerned with the study of the rolling without slipping of a dynamically symmetric (in particular, homogeneous) heavy ball on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are…

By considering the spin connection, we deduce the effective equation for a spin-1/2 particle confined to a curved surface with the non-relativistic limit and in the thin-layer quantization formalism. We obtain a pseudo-magnetic field and an…

The phenomenological Landau theory of the spin precession has been used to reproduce the out-of-equilibrium properties of many magnetic systems. However, such an approach suffers from some serious limitations. The main reason is that the…

We present a (possibly) new sphere eversion based on the contractibility* of a certain subset of the space of immersions of the circle in the plane. (*: by strong deformation retraction)

Several scenarios used in teaching feature a rolling motion with slipping that transitions to one without through friction with the ground. We summarise these transitions by introducing an unknown impulse that is transferred to the ground.…

At a macroscopic level, concepts such as top spin, back spin and rolling are commonly used to describe the collision of balls and surfaces. Each term refers to an aspect of the coupling of rotational motion during the collision of a…

When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as…

A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…

We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally…

We formulate a non-relativistic Hamiltonian in order to describe how the rotational degrees of freedom of a dielectric sphere and quantized light fields are coupled. Such an interaction is shown to take a form of angular momentum coupling…

We study the diffusion of Brownian particles on the surface of a sphere and compute the distribution of solid angles enclosed by the diffusing particles. This function describes the distribution of geometric phases in two state quantum…

We provide a general formulation of the spin-orbit coupling on a 2D curved surface. Considering the wide applicability of spin-orbit effect in spinor-based condensed matter physics, a general spin-orbit formulation could aid the study of…

A vortex, a circulating flow around a void, is one of the basic topological phenomena in nature. Here we show that vortices generally emerge in spin wave travelling upon topologically nontrivial magnetic texture, due to the transverse…