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In a set of experiments, Couder et. al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. We present a dynamical systems model, in the form of an iterative map, for a…
We study experimentally the dynamics of a water droplet on a tilted and vertically oscillating rigid fibre. As we vary the frequency and amplitude of the oscillations the droplet transitions between different modes: harmonic pumping,…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
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…
We consider a particle that is subject to a constant force and scatters inelastically on a vibrating periodically corrugated floor. At small friction and small radius of the circular scatterers the dynamics is dominated by resonances…
Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic…
This paper investigates the behavior of a heavy soft spring in steady circular motion. Since the spring is inhomogeneous due to centrifugal force, one can rigorously prove that it follows the one-dimensional static Willis-form equations.…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
The drag forces acting on a single polystyrene sphere in the vicinity of an oscillating glass plate have been measured using an optical tweezer. The phase of the sphere is found to be a sensitive probe of the dynamics of the sphere. 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 a one dimensional elastic string as a set of massless beads interacting through springs characterized by anisotropic elastic constants. The string, driven by an external force, moves in a medium with quenched disorder. We…
Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than…
We investigate the dynamics of an ensemble of inelastic hard spheres confined between two horizontal plates separated a distance smaller than twice the diameter of the particles, in such a way that the system is quasi-two-dimensional. The…
A magnetic-mechanical oscillating system consists of two identical leaf springs, a non-magnetic base, and some magnets. The leaf springs are fixed at the bottom to the non-magnetic base, while the magnet is attached to the top of the leaf…
We report an experimental study of the statistical properties of vibrated granular rings. In this system, a linked rod and bead metallic chain in the form of a ring is collisionally excited by a vertically oscillating plate. The dynamics…
We study a layer of grains atop a plate which oscillates sinusoidally in the direction of gravity, using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order as well as hard-sphere molecular…
The swinging spring, or elastic pendulum, has a 2:1:1 resonance arising at cubic order in its approximate Lagrangian. The corresponding modulation equations are the well-known three-wave equations that also apply, for example, in…
The free motion of balls is investigated experimentally in continously stratified fluid in a finite container. The oscillation frequency is found to be very close to the local Brunt-Vaisala frequency. The effect of added mass proves to be…
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
In this article we study the dynamics of coupled oscillators. We use mechanical metronomes that are placed over a rigid base. The base moves by a motor in a one-dimensional direction and the movements of the base follow some functions of…