Classical Normal Modes in Damped Linear Dynamic Systems

1965 ◽  
Vol 32 (3) ◽  
pp. 583-588 ◽  
Author(s):  
T. K. Caughey ◽  
M. E. J. O’Kelly
Keyword(s):  
Dynamic Systems ◽  
Normal Modes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Necessary And Sufficient

The purpose of this paper is to determine necessary and sufficient conditions under which both discrete and continuous damped linear dynamic systems possess classical normal modes.

Normal and Quasi-Normal Modes in Damped Linear Dynamic Systems

1966 ◽  
Vol 33 (2) ◽  
pp. 413-416 ◽  
Author(s):  
J. S. Maybee
Keyword(s):  
Linear Systems ◽  
Dynamic Systems ◽  
Normal Modes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Necessary And Sufficient

A generalization of the concept of classical normal modes in damped linear systems is presented. It is then shown that a necessary and sufficient condition that such quasi-normal modes exist is that certain matrices associated with the system commute. Necessary and sufficient conditions of the same type are also obtained for the classical normal modes, but under more restrictive conditions.

scholarly journals Control of stage by stage changing linear dynamic systems

2012 ◽  
Vol 22 (1) ◽  
pp. 31-39 ◽  
Author(s):  
V.R. Barseghyan
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Time Intervals ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Necessary And Sufficient ◽  
Total Controllability

In this paper, the control problems of linear dynamic systems stage by stage changing and the optimal control with the criteria of quality set for the whole range of time intervals are considered. The necessary and sufficient conditions of total controllability are also stated. The constructive solving method of a control problem is offered, as well as the definitions of conditions for the existence of programmed control and motions. The explicit form of control action for a control problem is constructed. The method for solving optimal control problem is offered, and the solution of optimal control of a specific target is brought.

Classical Normal Modes in Damped Linear Dynamic Systems

1960 ◽  
Vol 27 (2) ◽  
pp. 269-271 ◽  
Author(s):  
T. K. Caughey
Keyword(s):  
Dynamic Systems ◽  
Necessary Conditions ◽  
Normal Modes ◽  
Present Theory ◽  
Necessary And Sufficient Condition ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Damping Matrix ◽  
Necessary And Sufficient ◽  
Special Case

An analysis of the conditions under which a damped linear system possesses classical normal modes is presented. It is shown that a necessary and sufficient condition for the existence of classical normal modes is that the damping matrix be diagonalized by the same transformation that uncouples the undamped systems. Sufficient though not necessary conditions on the damping matrix are developed, and it is shown that Rayleigh’s solution is a special case of the present theory.

On the Almost Sure Stability of Linear Dynamic Systems With Stochastic Coefficients

1965 ◽  
Vol 32 (2) ◽  
pp. 365-372 ◽  
Author(s):  
T. K. Caughey ◽  
A. H. Gray
Keyword(s):  
Nonlinear System ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Forced Oscillations ◽  
Almost Sure Stability ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

In this paper a Lyapunov type of approach is used to obtain sufficient conditions guaranteeing the almost sure stability of linear dynamic systems with stochastic coefficients. The results are generalized to include a certain class of nonlinear system and also to guarantee the almost sure boundedness of the forced oscillations of linear dynamic systems with stochastic coefficients.

Stability of Linear Dynamic Systems With Narrow-Band Parametric Excitation

1967 ◽  
Vol 34 (3) ◽  
pp. 709-713 ◽  
Author(s):  
T. K. Caughey ◽  
J. R. Dickerson
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Systems ◽  
Parametric Excitation ◽  
Narrow Band ◽  
Sufficient Conditions ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

A Lyapunov-type approach is used to establish sufficient conditions guaranteeing the asymptotic stability of a class of linear dynamic systems with bounded, narrow-band parametric excitation.

scholarly journals Impulsive Cluster Anticonsensus of Discrete Multiagent Linear Dynamic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Liping Zhang ◽  
Haibo Jiang
Keyword(s):  
Numerical Simulation ◽  
Dynamic System ◽  
Multiagent Systems ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Linear Dynamic System ◽  
Linear Dynamic Systems ◽  
Important Type ◽  
Linear Dynamic ◽  
Theoretical Results

Cluster anticonsensus is another important type consensus of multiagent systems. In this paper, we investigate the problem of impulsive cluster anticonsensus of discrete multiagent linear dynamic systems. Firstly, an impulsive protocol is designed to achieve the cluster anticonsensus. Then sufficient conditions are given to guarantee the cluster anticonsensus of the discrete multiagent linear dynamic system based on theQ-theory. Numerical simulation shows the effectiveness of our theoretical results.

scholarly journals Stochastic Controllability of Systems with Multiple Delays in Control

2009 ◽  
Vol 19 (1) ◽  
pp. 39-48 ◽  
Author(s):  
Jerzy Klamka
Keyword(s):  
Dynamic System ◽  
Dynamic Systems ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Multiple Delays ◽  
Stochastic Dynamic ◽  
Relative Controllability ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Controllability Of Systems

Stochastic Controllability of Systems with Multiple Delays in ControlFinite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with multiple point delays in control are considered. Using the notation, theorems and methods used for deterministic controllability problems for linear dynamic systems with delays in control as well as necessary and sufficient conditions for various kinds of stochastic relative controllability in a given time interval are formulated and proved. It will be proved that, under suitable assumptions, relative controllability of an associated deterministic linear dynamic system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamic system. As a special case, relative stochastic controllability of dynamic systems with a single point delay is also considered. Some remarks and comments on the existing results for stochastic controllability of linear dynamic systems are also presented.

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