Related papers: Inertial control of a spinning flat disk
We provide a short proof of the $L^2$-orbital stability of a class of explicit steady Euler flows in a disk by establishing a quantitative estimate. The main idea is to exploit the conserved quantities of the Euler equation, including the…
We apply an invariant-based inverse engineering method to control by time-dependent electric fields electron spin dynamics in a quantum dot with spin-orbit coupling in a weak magnetic field. The designed electric fields provide a shortcut…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
The so-called Landau-Levich-Deryaguin problem treats the coating flow dynamics of a thin viscous liquid film entrained by a moving solid surface. In this context, we use a simple experimental set-up consisting of a partially-immersed…
We apply methods of the so-called `inverse problem of the calculus of variations' to the stabilization of an equilibrium of a class of two-dimensional controlled mechanical systems. The class is general enough to include, among others, the…
This paper proposes a new adaptation methodology to find the control inputs for a class of nonlinear systems with time-varying bounded uncertainties. The proposed method does not require any prior knowledge of the uncertainties including…
We construct a family of rotating vortex patches with fixed angular velocity for the two-dimensional Euler equations in a disk. As the vorticity strength goes to infinity, the limit of these rotating vortex patches is a rotating point…
We derive a saturated feedback control, which locally stabilizes a linear reaction-diffusion equation. In contrast to most other works on this topic, we do not assume the Lyapunov stability of the uncontrolled system and consider general…
In this article we consider a 2-D quantum particle confined a disc whose radius can be deformed continuously in time. We study the problem of controllability of such a quantum particle via deformations of the initial disc, i.e., when we set…
The generalized Euler case (rigid body rotation over the fixed point) is discussed here: - the center of masses of non-symmetric rigid body is assumed to be located at the equatorial plane on axis Oy which is perpendicular to the main…
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…
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of $n$ rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
An "upward-driven disk" is a novel mechanical device built from LEGO parts. A circular disk is suspended from the point where it is sandwiched between two wheels, making it free to oscillate as a pendulum, but the location of that…
We propose a novel scheme to efficiently polarize and manipulate the electron spin in a quantum dot. This scheme is based on the spin-orbit interaction and it possesses following advantages: (1) The direction and the strength of the spin…
In this paper, an adaptive nonlinear strategy for the motion and force control of flexible manipulators is proposed. The approach provides robust motion control until contact is detected when force control is then available--without any…
Einstein-aether theory is extended by allowing for spinning degrees of freedom of the aether. In addition to the acceleration, shear, expansion, and vorticity of the aether velocity field, a spin rotation describing the dynamics of a…
We find equations of particle motion from the point of view of observer on a rotating disk, and demonstrate that a particle moving along a rotating disk is influenced by forces arising from geometry. They can be considered as analogs of the…
In this paper we study the origin of inertia in a curved spacetime, particularly the spatially flat, open and closed Friedmann universes. This is done using Sciama's law of inertial induction, which is based on Mach's principle, and…
The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also indicates a special case when an additional integral and…