
Accession Number : AD0669630
Title : STABILITY OF SOME NONLINEAR SYSTEMS,
Corporate Author : CALIFORNIA UNIV BERKELEY STRUCTURAL ENGINEERING LAB
Personal Author(s) : Mostaghel,Naser ; Sackman,Jerome L.
Report Date : FEB 1968
Pagination or Media Count : 75
Abstract : The stability of systems governed by x double dot + f(x) + q(x, x dot)x dot  phi(t) r(x) = S(x;t) is studied. Liapunov's Direct Method and a linearization approach have been used in the study of stability of the above system for phi(t) L sub 1 integrable, and periodic, respectively. In the former case a sufficiency region of stability is constructed through the use of a Liapunov function. In the latter case, which is investigated by means of a linearization process, a Hill equation is obtained, whose stability is studied by a method suggested by Malkin. Malkin's method is then modified to obtain, by use of a first approximation, the first stability region in parameter space. A second approximation is also worked out. When the approximations obtained herein for general periodic function are reduced to the special cases of the Mathieu equation and the Hill3term equation, the results compare very well with the available numerical results based on the exact solution of each of those equations. (Author)
Descriptors : (*BEAMS(STRUCTURAL), LOADS(FORCES)), STABILITY, NONLINEAR SYSTEMS, PERTURBATION THEORY, APPROXIMATION(MATHEMATICS), FOURIER ANALYSIS, DIFFERENTIAL EQUATIONS, SERIES(MATHEMATICS), INEQUALITIES, THEOREMS
Subject Categories : Theoretical Mathematics
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Distribution Statement : APPROVED FOR PUBLIC RELEASE