Numerical analysis of relative equilibrium states and its stability of a string system with a rigid body

1996 ◽  
Vol 1 (2) ◽  
pp. 62-66
Author(s):  
Jianhua Cheng ◽  
Junfeng Li ◽  
Zhaolin Wang ◽  
Qiaozhe Wu
Keyword(s):  
Numerical Analysis ◽  
Rigid Body ◽  
Relative Equilibrium ◽  
Equilibrium States

scholarly journals Numerical analysis of the drag on a rigid body in an immersed granular flow

2021 ◽  
Author(s):  
Nathan Coppin ◽  
Matthieu Constant ◽  
Jonathan Lambrechts ◽  
Frédéric Dubois ◽  
Vincent Legat
Keyword(s):  
Numerical Analysis ◽  
Rigid Body ◽  
Granular Flow

scholarly journals The Dynamical Behavior of a Rigid Body Relative Equilibrium Position

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
T. S. Amer
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Relative Equilibrium ◽  
Dynamical Behavior ◽  
Vertical Plane ◽  
The Body ◽  
Physical Parameters ◽  
Pendulum Model

In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange’s equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.

Testing and Numerical Analysis of Elastoplastic Steel Column Impacted by Rigid Body

2011 ◽  
Vol 4 (8) ◽  
pp. 2951-2956
Author(s):  
Yuzhi He ◽  
Changyun Liu ◽  
Xiugen Jiang ◽  
Zhenhua Hou ◽  
Guangkui Zhang ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Rigid Body ◽  
Steel Column

Oscillation of a Net Panel With Bending Stiffness

2013 ◽  
Author(s):  
Østen Jensen ◽  
Lars Gansel ◽  
Martin Føre ◽  
Karl-Johan Reite ◽  
Jørgen Haavind Jensen ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Numerical Model ◽  
Rigid Body ◽  
Polyethylene Terephthalate ◽  
Oscillation Amplitude ◽  
Bending Stiffness ◽  
Oscillatory Motion ◽  
Product Certification ◽  
Net Cages ◽  
Oscillation Frequencies

The behaviour of net panels with bending stiffness is dependent on the stiffness and potentially also the density of the material when exposed to oscillatory motions. This needs to be taken into account when net cages are product certified according to NS9415 (Standard Norge 2009). Experiments using two different net panels with bending stiffness were conducted to investigate the behaviour of nets with bending stiffness in oscillatory motion. For low oscillation frequencies the panels moved in a close to rigid body manner. When the oscillation frequencies where increased, however, there was a distinct difference between the copper and the Polyethylene Terephthalate (PET) nets, with a significant increase in the resulting oscillation amplitude for the copper net and a decrease for the PET net. The proposed numerical model predicts this behaviour well in terms of oscillation amplitudes. It is, however, important to establish good estimates of the net panels bending stiffness in advance, particularly if product certification is the purpose of the numerical analysis.

RELATIVE EQUILIBRIUM STATES AND DIMENSIONS OF FIBERWISE INVARIANT MEASURES FOR RANDOM DISTANCE EXPANDING MAPS

2013 ◽  
Vol 14 (01) ◽  
pp. 1350015 ◽  
Author(s):  
DAVID SIMMONS ◽  
MARIUSZ URBAŃSKI
Keyword(s):  
Invariant Measure ◽  
Invariant Measures ◽  
Gibbs State ◽  
Relative Equilibrium ◽  
Equilibrium States ◽  
Expanding Maps ◽  
Hölder Continuous ◽  
Random Maps ◽  
Full Dimension ◽  
Relative Metric

We show that the Gibbs states (known from [10] to be unique) of Hölder continuous potentials and random distance expanding maps coincide with relative equilibrium states of those potentials, proving in particular that the latter exist and are unique. In the realm of conformal expanding random maps, we prove that given an ergodic (globally) invariant measure with a given marginal, for almost every fiber the corresponding conditional measure has dimension equal to the ratio of the relative metric entropy and the Lyapunov exponent. Finally we show that there is exactly one invariant measure whose conditional measures are of full dimension. It is the canonical Gibbs state.

scholarly journals Relative equilibrium states and class degree

2017 ◽  
Vol 39 (4) ◽  
pp. 865-888
Author(s):  
MAHSA ALLAHBAKHSHI ◽  
JOHN ANTONIOLI ◽  
JISANG YOO
Keyword(s):  
Finite Type ◽  
Upper Bound ◽  
Relative Equilibrium ◽  
Ergodic Measure ◽  
Equilibrium States ◽  
Shift Of Finite Type ◽  
Sofic Shift ◽  
Ergodic Measures ◽  
Factor Code ◽  
Special Case

Given a factor code $\unicode[STIX]{x1D70B}$ from a shift of finite type $X$ onto a sofic shift $Y$, an ergodic measure $\unicode[STIX]{x1D708}$ on $Y$, and a function $V$ on $X$ with sufficient regularity, we prove an invariant upper bound on the number of ergodic measures on $X$ which project to $\unicode[STIX]{x1D708}$ and maximize the measure pressure $h(\unicode[STIX]{x1D707})+\int V\,d\unicode[STIX]{x1D707}$ among all measures in the fiber $\unicode[STIX]{x1D70B}^{-1}(\unicode[STIX]{x1D708})$. If $\unicode[STIX]{x1D708}$ is fully supported, this bound is the class degree of $\unicode[STIX]{x1D70B}$. This generalizes a previous result for the special case of $V=0$ and thus settles a conjecture raised by Allahbakhshi and Quas.

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