We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-stat...

The dynamics of a bead sliding without friction along a periodically pulsating wire is under consideration. If the arc length of the wire is taken as the relevant coordinate, the motion of the bead is described by a periodic newtonian equation. Sufficient conditions are derived assuring that a given equilibrium is of twist type, a property that implies its nonlinear stability as well as a KAM s...

This paper proposes a friction model parameter identification routine that can work with highly nonlinear and chaotic systems. The chosen system for this study is passively-actuated tilted Furuta pendulum, which known to have coupled model. pendulum ensure the existence of stable equilibrium configuration all its degrees freedom, link weights are only external forces applied system. A analytica...

A physical pendulum consisting of a circular disk at the end of a thin metal rod is connected to a low-friction rotary motion sensor, so that its angular position and velocity can be accurately measured. The disk can be oriented either perpendicular or parallel to the plane of swing to give significant or negligible air drag, respectively. The motion is analytically modeled in phase space. A qu...

The need for vibration isolation of precision and vibrationsensitive objects is increasing continuously. Vibration isolation systems must comply with contradictory specifications, such as requiring reduced stiffness of isolators for better isolation, but higher stiffness for better performance of the object. Recently, expensive active isolation systems have been used to resolve these contradict...

remotely control through the Internet. Our objective is threefold. We are attempting to provide an educational resource for chaos, demonstrate a new technology, and experiment with a new method of laboratory education. Figure 1 shows the pendulum control panel. As students vary the driving frequency, they can watch the pendulum's motion switch from simple periodic motion to chaotic motion. The ...

This paper is a continuation of the article «Optimization oscillation damping modes spatial double pendulum. I. Formulation problem», in which problem formulation optimal oscillations pendulum with joint axes not collinear to each other was given. Passive (viscous friction) considered separately, and possibility additional accounting active impacts (collinear control) also discussed. Two optimi...

This paper presents an extensive experimental study of a low-cost, high-performance seismic isolator comprising deformable sphere rolling on concrete surfaces. Polyurethane spheres, with and without steel core, flat or spherical plates, are investigated. Lateral cyclic tests under large displacements demonstrated friction coefficient between 3.7% 7.1%. When tested in shake table 1170 ground mot...

The paper discusses the issues of optimal damping oscillations a spatial double pendulum, whose joint axes are not collinear to each other. As options for damping, both simply passive associated with influence viscous friction, and combined active considered, influences formed according principle control. analytical solution system motion equations is given cases in framework linear model, it c...

A frequency domain dynamic analysis is needed to obtain the response of structures constructed on a system of base isolators on flexible soil when subjected to earthquake ground motion. In such systems, the lateral stiffness of the base isolators is so small, compared to the structural stiffness, that in an earthquake attack the fundamental vibration mode dominates the response. With this in mi...