Related papers: Asymptotics of Maxwell time in the plate-ball prob…
The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…
The problem of a disc and a ball rolling on a horizontal plane without slipping is considered. Differential constrained equations are shown to be integrated when the trajectory of the point of contact is taken in a form of the natural…
We establish an instructive experiment to investigate the minimum time curve traveled by a small billiard ball rolling in a grooved track under gravity. Our intention is to popularize the concept of \textit{minimum time curve} anew, and to…
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
We study the rolling motion of a small solid sphere on a surface patterned rubber substrate in an external field with and without a noise. In the absence of the noise, the ball does not move below a threshold force above which it…
When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order…
A general approach to a broad class of asymptotic problems related to long-time influence of small perturbations, of both deterministic and stochastic type, is presented in the paper. The main characteristic of this influence is a limiting…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…
This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not…
This paper presents estimates for the distribution of the exit time from balls and short time asymptotics for measure metric Dirichlet spaces. The estimates cover the classical Gaussian case, the sub-diffusive case which can be observed on…
We apply Maxwell and Cattaneo's relaxation approaches to the analysis of strong shockwaves in a two-dimensional viscous heat-conducting fluid. Good agreement results for reasonable values of Maxwell's relaxation times. Instability results…
This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the…
We study the rolling of the Chaplygin ball in $\mathbb R^n$ over a fixed $(n-1)$--dimensional sphere without slipping and without slipping and twisting. The problems can be naturally considered within a framework of appropriate…
An inductive procedure is developed to calculate the asymptotic behavior at time zero of a diffusion with polynomial drift and degenerate, additive noise. The procedure gives rise to two different rescalings of the process; namely, a…
The motion of a thin elastic plate interacting with a viscous fluid is investigated. A periodic force acting on the plate is considered, which in a setting without damping could lead to a resonant response. The interaction with the viscous…
We consider 2D Maxwell-Lorentz equations with extended charged rotating particle. The system admits solitons which are solutions corresponding to a particle moving with a constant velocity and rotating with a constant angular velocity. Our…
We study the scattering relation and the sojourn times on non-trapping asymptotically hyperbolic manifolds and use it to obtain the asymptotics of the distance function on geodesically convex asymptotically hyperbolic manifolds.
We develop an asymptotical control theory for one of the simplest distributed oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of string states that admit…
New measurements are presented of the lift on a spinning baseball. The experiment utilizes a pitching machine to project the baseball horizontally; a high-speed motion capture system to measure the initial velocity and angular velocity and…
An outline is given of recent work concerning the electromagnetic duality properties of Maxwell theory on curved space-times with or without spin structures.