On the stability of the equilibrium state and small oscillations of non-holonomic systems

1994 ◽  
Vol 9 (1) ◽  
pp. 3-17
Author(s):  
Lilong Cai
Keyword(s):  
Equilibrium State ◽  
Small Oscillations ◽  
Holonomic Systems ◽  
The Stability

The Stability of a Simple Surge Tank

1968 ◽  
Vol 90 (1) ◽  
pp. 97-102
Author(s):  
R. K. Duggins
Keyword(s):  
Steady State ◽  
Operating Conditions ◽  
Laboratory Model ◽  
Surge Tank ◽  
Hydraulic Power ◽  
Small Oscillations ◽  
The Stability ◽  
Surge Phenomena ◽  
Small Disturbances

An equation is derived to describe small oscillations in a simple surge tank for a wider range of operating conditions than hitherto considered. It is presented in a new non-dimensional form which facilitates an immediate prediction of surge phenomena when small disturbances are imposed on any given set of steady-state conditions. A characteristic of general form is assumed for conduit friction, and the effect is considered of deviation from the condition of constant hydraulic power delivered to the turbine. Some experiments have been carried out with a laboratory model simulating a variety of steady-state operating conditions, and surge measurements are presented for comparison with the calculated behavior.

Equilibrium State of Football Players Affected by Disturbance

2014 ◽  
Vol 933 ◽  
pp. 291-294
Author(s):  
Chun Ping Dong
Keyword(s):  
Equilibrium State ◽  
The Body ◽  
Equilibrium Strategy ◽  
Football Players ◽  
Body Measurement ◽  
Recovery Strategy ◽  
Theoretical Support ◽  
Standing Up ◽  
Human Balance ◽  
The Stability

Strategies of human balance when standing up from static equilibrium strategy began. The paper use bio-mechanical principles study human balance strategies, we will first discuss the stability of the human body measurement problems, and then discuss the footballer walking process disturbed the balance of input recovery strategy, and the results of this study provide enhancements for the body to balance the theoretical support.

NORMALIZATION IN THE SYSTEMS WITH SMALL DIFFUSION

1996 ◽  
Vol 06 (06) ◽  
pp. 1093-1109 ◽  
Author(s):  
S. A. KASCHENKO
Keyword(s):  
Equilibrium State ◽  
Stability Problem ◽  
Critical Case ◽  
Evolution Equations ◽  
Normal Forms ◽  
Initial Problem ◽  
Nonlinear Pdes ◽  
Small Diffusion ◽  
The Stability

In this paper the local dynamics of systems of nonlinear PDEs with small diffusion is studied. The main feature of these systems lies in the fact that the dimension of a critical case in the stability problem for an equilibrium state is equal to infinity. Algorithms that reduce the initial problem to the analysis of nonlocal dynamics of special evolution equations playing the role of normal forms are developed.

scholarly journals Stability Analysis of Swarm Heterogeneous Robots with Limited Field of View

2020 ◽  
Vol 19 (5) ◽  
pp. 942-966
Author(s):  
Takahiro Endo ◽  
Ryuma Maeda ◽  
Fumitoshi Matsuno
Keyword(s):  
Stability Analysis ◽  
Equilibrium State ◽  
Maximum Velocity ◽  
Field Of View ◽  
Robot Swarms ◽  
Swarm Robots ◽  
Heterogeneous Robots ◽  
Physical Limitations ◽  
The Stability ◽  
Navigation Method

This paper presents a stability analysis of swarm robots, a group of multiple robots. In particular, we focus on robot swarms with heterogeneous abilities, in which each robot has a different sensing range and physical limitations, including maximum velocity and acceleration. In addition, each robot has a unique sensing region with a limited angle field of view. We previously proposed a decentralized navigation method for such heterogeneous swarm robots consisting of one leader and multiple followers. With the decentralized navigation method, a single leader can navigate for followers while maintaining connectivity and satisfying the physical limitations unique to each robot; i.e., each follower has a target robot and follows it without violating its physical limitations. In this paper, we focus on a stability analysis of such swarm robots. When the leader moves at a constant velocity, we mathematically prove that the shape and orientations of all robots eventually converge to the equilibrium state. For this, we must first prove that the equilibrium state exists. Then, we show the convergence of the state to its equilibrium. Finally, we carry out experiments and numerical simulations to confirm the stability analysis, i.e., the convergence of the swarm robots to the equilibrium states.

scholarly journals The use of Catastrophe Theory to Analyse the Stability and Toppling of Icebergs

1980 ◽  
Vol 1 ◽  
pp. 49-54 ◽  
Author(s):  
J. F. Nye ◽  
J. R. Potter
Keyword(s):  
Catastrophe Theory ◽  
Three Dimensional ◽  
Theory Approach ◽  
Rectangular Section ◽  
Small Oscillations ◽  
Density Distributions ◽  
Conceptual Clarity ◽  
Different Shapes ◽  
The Stability ◽  
The Individual

As an iceberg melts, the resulting change of shape can cause it to list gradually or to become unstable and topple over suddenly. Similarly, when an iceberg breaks up some of the individual pieces may capsize. We have used Zeeman’s analysis of the stability of ships, which is based on catastrophe theory, to examine this problem. We deal only with statical equilibrium; dynamical effects induced by water motion are important for ships, but very large icebergs have correspondingly small oscillations and therefore dynamical aspects are ignored in this first study. The advantage of the catastrophe-theory approach over the conventional stability theory used by naval architects lies in the conceptual clarity that it provides. In particular, it gives a three-dimensional geometrical picture that enables one to see all the possible equilibrium attitudes of a given iceberg, whether they are stable or unstable, whether a stable attitude is dangerously close to an unstable one, and how positions of stable equilibrium can be destroyed as the shape of the iceberg evolves with time.By making two-dimensional computations we examine the stability of two different shapes of cross-section, rectangles and trapezia, with realistic density distributions. These shapes may list gradually or topple suddenly as a single parameter is changed. For example, we find that a conversion of the vertical sides of a rectangular section into the slightly inward-sloping sides of a trapezium has a comparatively large adverse effect on stability. The main purpose of this work is to suggest how the stability characteristics of any selected iceberg may be investigated systematically.

Coexisting Infinitely Many Nonchaotic Attractors in a Memristive Weight-Based Tabu Learning Neuron

2021 ◽  
Vol 31 (12) ◽  
pp. 2150189
Author(s):  
Liping Hou ◽  
Han Bao ◽  
Quan Xu ◽  
Mo Chen ◽  
Bocheng Bao
Keyword(s):  
Equilibrium State ◽  
Printed Circuit Board ◽  
Synaptic Weight ◽  
Circuit Board ◽  
Initial State ◽  
Printed Circuit ◽  
Extreme Multistability ◽  
Physical Processing ◽  
The Stability ◽  
Line Equilibrium

Memristive synaptic weight is a changeable connection synaptic weight. It reflects the self-adaption physical processing in biological neurons. To study its dynamical effect, this paper presents a memristive synaptic weight-based tabu learning neuron model. It is constructed by replacing the resistive self-connection synaptic weight in the tabu learning neuron with a memristive self-connection synaptic weight. The equilibrium point of the memristive tabu learning model is time-varying and switches between no equilibrium state and line equilibrium state with the change of the external current. Particularly, the stability of the line equilibrium state closely relies on the initial state of the memristor, resulting in the emergence of coexisting infinitely many nonchaotic attractors. By employing the bifurcation plots, Lyapunov exponents, and phase plots, this paper numerically reveals the initial state-switched coexisting bifurcation behaviors and initial state-relied extreme multistability, and thereby discloses the coexisting infinitely many nonchaotic attractors composed of mono-periodic, multiperiodic, and quasi-periodic orbits. In addition, PSIM circuit simulations and printed-circuit board-based experiments are executed and the coexisting infinitely many nonchaotic attractors are realized physically. The results well verify the numerical simulations.

scholarly journals Dynamics of a New Strain of the H1N1 Influenza A Virus Incorporating the Effects of Repetitive Contacts

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Puntani Pongsumpun ◽  
I-Ming Tang
Keyword(s):  
Stability Analysis ◽  
Equilibrium State ◽  
Influenza A Virus ◽  
Influenza A ◽  
Present Model ◽  
Numerical Solutions ◽  
H1n1 Influenza ◽  
Dynamical Modeling ◽  
Mathematical Equations ◽  
The Stability

The respiratory disease caused by the Influenza A Virus is occurring worldwide. The transmission for new strain of the H1N1 Influenza A virus is studied by formulating a SEIQR (susceptible, exposed, infected, quarantine, and recovered) model to describe its spread. In the present model, we have assumed that a fraction of the infected population will die from the disease. This changes the mathematical equations governing the transmission. The effect of repetitive contact is also included in the model. Analysis of the model by using standard dynamical modeling method is given. Conditions for the stability of equilibrium state are given. Numerical solutions are presented for different values of parameters. It is found that increasing the amount of repetitive contacts leads to a decrease in the peak numbers of exposed and infectious humans. A stability analysis shows that the solutions are robust.

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