相关论文: Motion of a system of oscillators under the genera…

The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…

We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of…

The dynamical behavior caused by dry friction is studied for a spring-block system pulled with constant velocity over a surface. The dynamical consequences of a general type of phenomenological friction law (stick-time dependent static…

The article studies the transport equation that governes the motion of a fluid in a bounded domain, under the hypothesis of zero velocity at the boundary and supposing the incompressible nature of the fluid. Together with existence and…

Dry friction has been proposed as a rectifying mechanism allowing mass transport over a vibrating surface, even when vibrations are horizontal and unbiased. It has been suggested that the drift velocity will always saturate when the energy…

Two different controlling methods are proposed to stabilize unstable continuous-sliding states of a dry-friction oscillator. Both methods are based on a delayed-feedback mechanism well-known for stabilizing periodic orbits in deterministic…

We consider a particle on the horizontal plane with a dry friction. The friction is anisotropic but symmetric under the group of rotations of the plane. It turns out that the particle can move such that in the finite time the trajectory…

The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…

An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…

The motion of a vertically positioned bicycle is considered when a horizontal control force, which maybe both internal and external in relation to the bicycle, is applied to its pedal. Tangential forces of dryfriction obeying the Euler {…

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry (Coulombic) friction coupled to asymmetric…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

We demonstrate existence in the ``large" and uniqueness in the ``small" of equilibrium configurations for the coupled system consisting of a Navier-Stokes fluid interacting with a rigid body subjected to spring forces and restoring moments.…

There exist some boundary-driven open systems with diffusive dynamics whose particle current fluctuations exhibit universal features that belong to the Edwards-Wilkinson universality class. We achieve this result by establishing a mapping,…

In this paper, we study the unitary Dyson Brownian motion through a partial differential equation approach recently introduced for the real Dyson case. The main difference with the real Dyson case is that the spectrum is now on the circle…

We consider a point mass on a horizontal plane. The motion of the plane is given. The plane moves periodically such that all its points have congruent closed trajectories. There is the Coulomb friction between the point mass and the plane.…

For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic…

Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…

Recent model simulations discovered unexpected non-monotonic features in the wear-free dry phononic friction as a function of the sliding speed. Here we demonstrate that a rather straight- forward application of linear-response theory,…

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…