scholarly journals Erratum: “On the Stability of Steady Motions in Free and Restrained Dynamical Systems” (Journal of Applied Mechanics, 1979, 46, pp. 427–432)

1980 ◽  
Vol 47 (2) ◽  
pp. 462-462
Author(s):  
P. Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Applied Mechanics ◽  
The Stability ◽  
Steady Motions

An Instability Theorem for Steady Motions in Free and Restrained Dynamical Systems

1980 ◽  
Vol 47 (4) ◽  
pp. 908-912 ◽  
Author(s):  
P. Hagedorn ◽  
W. Teschner
Keyword(s):  
Dynamical Systems ◽  
Stability Behavior ◽  
Two Systems ◽  
The Stability ◽  
Steady Motions

The stability of steady motions in dynamical systems with ignorable coordinates is considered. In addition to the original “free” systems “restrained” systems are defined in such a way that the ignorable velocities remain constant along all motions; the stability behavior of the two systems is compared. A previously established instability theorem is generalized and three examples are given.

On the Stability of Steady Motions in Free and Restrained Dynamical Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 427-432 ◽  
Author(s):  
P. Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Stability Behavior ◽  
Stability And Instability ◽  
Heavy Gyrostat ◽  
The Stability ◽  
Steady Motions

In this paper the stability of the steady motions of dynamical systems with ignorable coordinates is considered. In addition to the original “free” systems “restrained” systems are defined in such a way that the ignorable velocities remain constant for all motions. The relation between the stability behavior of these two types of systems is examined in detail and several stability and instability theorems are given for damped and undamped systems. An illustrative example deals with the steady motions of a heavy gyrostat.

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

A novel approach for the stability problem in non-linear dynamical systems

2003 ◽  
Vol 155 (1) ◽  
pp. 21-30 ◽  
Author(s):  
Tarcı́sio M. Rocha Filho ◽  
Iram M. Gléria ◽  
Annibal Figueiredo
Keyword(s):  
Dynamical Systems ◽  
Stability Problem ◽  
Linear Dynamical Systems ◽  
Novel Approach ◽  
Non Linear ◽  
The Stability

SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR

2013 ◽  
Vol 23 (03) ◽  
pp. 1330009 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
MOZHDEH S. FARAJI MOSADMAN
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Degrees Of Freedom ◽  
Eigenvalue Analysis ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.

Large-Scale Uncertain Systems Under Insufficient Decentralized Controllers

1989 ◽  
Vol 111 (3) ◽  
pp. 359-363 ◽  
Author(s):  
Y. H. Chen
Keyword(s):  
Dynamical Systems ◽  
Uncertain Systems ◽  
Large Scale ◽  
Large Scale System ◽  
Uncertain Dynamical Systems ◽  
Partial Stability ◽  
Decentralized Controllers ◽  
Total Stability ◽  
The Stability

We consider a class of large-scale uncertain dynamical systems under decentralized controllers. The system is composed of N interconnected subsystems which possess uncertainty. Moreover, there are uncertainties in the interconnections. If the subsystems are under sufficient decentralized controllers, the large-scale system is practically stable. As certain controllers fail, study on the conditions for total stability of partial stability to be preserved is made. It can be shown that the stability is only related to bound of uncertainty and the structure of the large-scale system. Moreover, the conditions can be utilized to determine the importance of some controllers for stability.

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