Criteria of Stability for Equilibriums Described by Polynomial Characteristic Equations
Journal Title: Romanian Journal of Acoustics and Vibration - Year 2013, Vol 10, Issue 2
Abstract
In this paper are given some new criteria of stability for the equilibrium positions obtained by solving third, fourth and fifth degrees polynomials. These equations appear when the equation of motion has the form ẍ=f(x), in which x=D=Rn, while f is a vector function, f:D→Rn. In this paper, the criteria are obtained using the Sturm sequence and they are completely developed for the polynomials of third, fourth and fifth degrees. For the common use, there are also plotted the diagram of the simply stability and sections through it with different planes for the case of the third degree polynomial, or simply sections through the diagrams of the simply stability using different hyper-planes or combinations of hyper-planes for the cases of the fourth or the fifth degrees polynomials. The domains of the simply stability are very complicated and their frontiers are impossible to describe in an analytical way. Practically, both analytical conditions and diagrams of simply stability may be used to determine if an equilibrium position is or is not simply stable. Numerical examples are also presented.
Authors and Affiliations
Nicolae STANESCU
Keywords
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