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 Hill-3-term 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