Nonlinear Dynamical Analysis of the “Power Ball”

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Tsuyoshi Inoue ◽  
Kohei Okumura ◽  
Kentaro Takagi
Keyword(s):  
Dynamical Behavior ◽  
Basin Of Attraction ◽  
First Integral ◽  
Dynamical Analysis ◽  
Rolling Motion ◽  
Precession Angle ◽  
Nonlinear Dynamical ◽  
Synchronous Rolling ◽  
Nonlinear Dynamical Analysis ◽  
The Basin Of Attraction

The gyroscopic exercise tool called the “Power Ball,” used to train the antebrachial muscle, is focused on. The basin of attraction of the synchronous rolling motion in the state space of initial condition is investigated. The reduced model governing the synchronous rolling motion is used and its averaged equation is deduced. The first integral for the dynamical behavior of the synchronous rolling motion occurring in the power ball is obtained. The separatrix, which identifies the basin of attraction of the synchronous rolling motion, is derived, and the ranges of initial precession angle and the initial spin angular velocity for realizing the synchronous rolling motion are clarified. These theoretically obtained results are then experimentally confirmed. Furthermore, the influences of parameters to the basin of attraction are also clarified.

scholarly journals Nonlinear Dynamical Analysis for the Cable Excited with Parametric and Forced Excitation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
C. Z. Qian ◽  
C. P. Chen ◽  
G. W. Zhou
Keyword(s):  
Dynamical Behavior ◽  
Vertical Vibration ◽  
Dynamical Analysis ◽  
Nonlinear Structure ◽  
Nonlinear Dynamical ◽  
Vibration Effect ◽  
Cable Stayed Bridge ◽  
Nonlinear Dynamical Analysis ◽  
Parameters Analysis ◽  
Forced Excitation

Considering the deck vibration effect on the cable in cable-stayed bridge, using nonlinear structure dynamics theory, the nonlinear dynamical equation for the stayed cable excited with deck vibration is proposed. Research shows that the vertical vibration of the deck has a combined parametric and forced excitation effect on the cable when the angle of the cable is taken into consideration. Using multiscale method, the 1/2 principle parametric resonance is studied and the bifurcation equation is obtained. Despite the parameters analysis, the bifurcation characters of the dynamical system are studied. At last, by means of numerical method and software MATHMATIC, the effect rules of system parameters to the dynamical behavior of the system are studied, and some useful conclusions are obtained.

scholarly journals Nonlinear dynamical analysis of carbachol induced hippocampal oscillations in mice

2009 ◽  
Vol 30 (6) ◽  
pp. 859-867 ◽  
Author(s):  
Metin Akay ◽  
Kui Wang ◽  
Yasemin M Akay ◽  
Andrei Dragomir ◽  
Jie Wu
Keyword(s):  
Dynamical Analysis ◽  
Nonlinear Dynamical ◽  
Nonlinear Dynamical Analysis

A Beam Element for Geometric Nonlinear Dynamical Analysis

2014 ◽  
Vol 919-921 ◽  
pp. 1273-1281
Author(s):  
Jin Duan ◽  
Yun Gui Li
Keyword(s):  
Three Dimensional ◽  
Beam Element ◽  
Dynamical Analysis ◽  
Elastic Deformations ◽  
Nonlinear Dynamical ◽  
Geometric Nonlinear ◽  
Nonlinear Dynamical Analysis ◽  
Updated Lagrangian ◽  
Incremental Equations ◽  
The Continuum

In this paper, a three-dimensional beam element is developed for geometric nonlinear dynamical analysis. This element is based on the co-rotational formulation, in which the displacements of beam element are subdivided into rigid body movements and elastic deformations. The formulations are derived from the continuum mechanics based Updated Lagrangian incremental equations. The element can undergo large deflections and rotations, but small strains are assumed in the deduction. The validity of this element is confirmed by comparing with the numerical results in other literatures.

108. Nonlinear dynamical analysis by Kaplan–Yorke Dimension of the effect by six stimuli on electroencephalograph

2009 ◽  
Vol 120 (5) ◽  
pp. e171
Author(s):  
Hirotoki Kawasaki ◽  
Takanobu Morinushi ◽  
Morinkuni Tkigawa ◽  
Shigeru Kanou ◽  
Masaru Yakushiji
Keyword(s):  
Dynamical Analysis ◽  
Nonlinear Dynamical ◽  
Nonlinear Dynamical Analysis
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