相关论文: The Precessing Top

It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light $c$ is the unit of velocity allows to cast all…

Symmetrical top is a special case of a general top. The canonical Poisson structure on T*SE(3) is the common method of its description. This Poisson structure is invariant under the right action of SO(3). However the Hamiltonian of the…

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…

We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both…

We recently studied spin precession in various stationary and axisymmetric spacetimes and applied it to the case of neutrinos propagating in those spacetimes. In this paper, the study of spin precession is extended to the case of a spinning…

Equations of a rotating body with one point constrained to move freely on a plane (dancing top) are deduced from the Lagrangian variational problem. They formally look like the Euler-Poisson equations of a heavy body with fixed point,…

The undulating metric tensors of general relativity do not possess a special and common velocity of propagation. Indeed, their velocity can even coincide with the speed of thought.

Observations of several protostellar jets show systematic differences in radial velocity transverse to the jet propagation direction, which have been interpreted as evidence of rotation in the jets. In this paper we discuss the origin of…

Einstein's perihelion advance formula can be given a geometric interpretation in terms of the curvature of the ellipse. The formula can be obtained by splitting the constant term of an auxiliary polar equation for an elliptical orbit into…

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the…

General relativity provides an appropriate framework for addressing the issue of sub- or superluminality as an apparent effect. Even though a massless particle travels on the light cone, its average velocity over a finite path measured by…

Application of the intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few new discretizations of motion of the Euler top sharing…

Velocity relaxation of a spherically symmetric polymer, immersed in a viscous incompressible fluid, and after a sudden small impulse or a sudden twist from a state of rest, is studied on the basis of the linearized Navier-Stokes equations…

The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…

A new object, called the velocity tensor, is introduced. It allows to formulate a generally covariant mechanics. Some properties of the velocity tensor are derived.

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion,…

We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both nonlinear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with…

We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…

A straightforward analytical scheme is proposed for computing the long-time, asymptotic mean velocity and dispersivity (effective diffusivity) of a particle undergoing a discrete biased random walk on a periodic lattice amongst an array of…

Precession is one of the important mechanisms of gravitational wave generation in astrophysics. In general, free precession of a rigid body can be caused by the rotation of a triaxial body. In the case of symmetric body, if only the…