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Nonlinear relaxation dynamics of a vertically-vibrated granular pile is experimentally studied. In the experiment, the flux and slope on the relaxing pile are measured by using a high-speed laser profiler. The relation of these quantities…
In this work, we consider a transmission problem describing a thermoelastic plate surrounding a membrane without any mechanical damping. The main results consist of the lack of exponential stability for this problem and the polynomial…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
Concept of curvature of liquid surrounding a spherical surface seems obvious in daily life, but based on earthly conditions everywhere. However, our understanding about the concept seems more transparent when we keep the system out of the…
This paper presents a methodology to stabilize some kind of Nonlinear Control system known as Driftless, utilizing the concept of \textit{Pseudo-Kinetic Energy} introduced in this work. Once this controller is applied to the Unicycle-type…
We have developed a toy model of flying snake's glide [J.J. Socha, Nature vol. 418 (2002) 603.] by modifying a model for a falling paper. We have found that asymmetric oscillation is a key about why snake can glide. Further investigation…
We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \begin{equation*} \partial_t^2\phi -\partial_x^2\phi + W'(\phi) = 0, \quad (t,x)\in\mathbb{R}\times\mathbb{R}. \end{equation*} The orbital…
We analyze the motion of a rod floating in a weightless environment in space when a force is applied at some point on the rod in a direction perpendicular to its length. If the force applied is at the centre of mass, then the rod gets a…
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…
The absence of any tendency toward rotation in a moving right angle lever is given a simple explanation.
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct…
We examine the derivation of the spin-orbit force from the Skyrme model. We find substantial agreement with phenomenological potentials. We show that a systematic and simultaneous treatment of all components of the kinetic energy introduces…
Louis Poinsot has shown in 1854 that the motion of a rigid body, with one of its points fixed, can be described as the rolling without slipping of one cone, the 'body cone', along another, the 'space cone', with their common vertex at the…
This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with…
In the problem of cylinder rolling without slipping on a horizontal floor, both the cylinder and floor are generally treated as rigid bodies in normal textbooks. When the air resistance is ignored, the equation of motion has a solution with…
We study numerically stick slip motions in a model of blocks and springs being pulled slowly. The sliding friction is assumed to change dynamically with a state variable. The transition from steady sliding to stick-slip is subcritical in a…
This paper tackles a friction compensation problem without using a friction model. The unique feature of the proposed friction observer is that the nominal motor-side signal is fed back into the controller instead of the measured signal. By…
Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being…
Models of a playground swing have been studied since the 1960s. However, in most of them, the position of the swinger is controlled directly. This simplifies the problem but hides the mechanics of torques applied to keep the swing moving in…
A ball rolled over a shallow step will experience an increase in velocity along the direction perpendicular to the step. This causes a deflection in the ball's trajectory. In this paper we derive the equations that describe the motion of a…