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Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…
We consider a randomly flashing ratchet, where the potential acting can be switched to another at random. Using coupled Fokker-Planck equations, we formulate the expressions of quantities measuring dynamics and thermodynamics. Extended…
The variation of the velocity of a periodic signal and its frequency along the world line of a standard emitter (at rest with an observer) are considered in a space with affine connections and metrics. It is shown that the frequency of the…
The helicon antenna is a well-known device in the field of electric propulsion. Here we investigate the vector potential produced in vacuum by such an antenna with typical size parameters. Both a static and a dynamic analysis are performed.…
The restricted three-vortex problem is investigated with one of the point vortices fixed in the plane. The motion of the free vortex having zero circulation is explored from a rotating frame of reference within which the free vortex with…
Putting several hard balls into a two-dimensional bowl can form a very basic two-dimensional model of hard-ball system. When the two-dimensional bowl has a parallel-rotation at a uniform speed around a center, when the number of balls is…
The motion of a bead on a rotating circular hoop is investigated using elementary calculus and simple symmetry arguments. The peculiar trajectories of the bead at different speeds of rotation of the hoop are presented. Phase portraits and…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
Bound vesicles subject to lateral forces such as arising from shear flow are investigated theoretically by combining a lubrication analysis of the bound part with a scaling approach to the global motion. A minor inclination of the bound…
We study the role of unsteady lift in the context of flapping wings in birds' flight. Both aerodynamicists and biologists attempt to address this subject, yet it seems that the contribution of the unsteady lift still holds many open…
We demonstrate the control of vortical motion of neutral classical particles in driven superlattices. Our superlattice consists of a superposition of individual lattices whose potential depths are modulated periodically in time but with…
The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a…
The existence of radial solutions of a nonlinear Dirichlet problem in a ball is translated to the language of Mechanics, i.e. to requirements on the time of motion of a particle in an external potential and under the action of a viscosity…
In the Ehrenfest wind tree model, a point particle moves on the plane and collides with randomly placed fixed square obstacles under the usual law of geometric optics. The particle represents the wind and the squares are the trees. We…
The problem of a bouncing ball on a non-planar surface is investigated. We discovered that surface undulation adds a horizontal component to the impact force, which acquires a random character. Some aspects of Brownian motion are found in…
We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being…
A layer of granular material on a vertically vibrating sawtooth-shaped base exhibits horizontal flow whose speed and direction depend on the parameters specifying the system in a complex manner. Discrete-particle simulations reveal that the…
We call a system bouncing ball billiard if it consists of a particle that is subjected to a constant vertical force and bounces inelastically on a one-dimendional vibrating periodically corrugated floor. Here we choose circular scatterers…
This paper addresses the problem of the Chaplygin ball rolling on a horizontal plane which rotates with constant angular velocity. In this case, the equations of motion admit area integrals, an integral of squared angular momentum and the…
We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…