Related papers: A Ball in a Groove
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and…
One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range…
We study the effect of viscoelastic dynamics on the frictional properties of a (mean field) spring-block system pulled on a rough surface by an external drive. When the drive moves at constant velocity V, two dynamical regimes are observed:…
A first-principle continuum-mechanics expression for the rolling friction coefficient is obtained for the rolling motion of a viscoelastic sphere on a hard plane. It relates the friction coefficient to the viscous and elastic constants of…
A simple text book problem in mechanics\cite{klep}, describes a massive horizontal bar placed on two oppositely rotating rollers, kept at a fixed center to center distance. Subsequent motion is to be found out in presence of kinetic…
Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results…
The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop…
When a viscoelastic shear-thinning drop of high elasticity hits a superhydrophobic surface, a growing tail-like filament vertically emerges from the impact spot as the contact line recedes. Notably, the ligament transitions into a…
A small sphere placed on the top of a big static frictionless sphere, slips until it leaves the surface at an angle $\theta_{l}=\cos^{-1}{2/3}$. On the other extreme, if the surface of the big sphere has coefficient of static friction,…
We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…
A two-dimensional earthquake model that consists of a single block resting upon a slowly moving rough surface and connected by two springs to rigid supports is studied. Depending on the elastic anisotropy and the friction force three…
The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which -when the bending elasticity…
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…
This article is devoted to the stabilization of two underactuated planar systems, the well-known straight beam-and-ball system and an original circular beam-and-ball system. The feedback control for each system is designed, using the Jordan…
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…
We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state.…
A small drop of a heavier fluid may float on the surface of a lighter fluid supported by surface tension forces. In equilibrium, the drop assumes a radially symmetric shape with a circular triple-phase contact line. We show theoretically…
We construct time independent configurations of two gravitating elastic bodies. These configurations either correspond to the two bodies moving in a circular orbit around their center of mass or strictly static configurations.