
Accession Number : AD0264058
Title : AN INVESTIGATION OF ONE NONLINEAR SYSTEM OF THREE DIFFERENTIAL EQUATIONS
Corporate Author : TRW SPACE TECHNOLOGY LABS LOS ANGELES CALIF
Personal Author(s) : PLISS,V.A.
Report Date : MAY 1961
Pagination or Media Count : 1
Abstract : Statements (without proof) are given for two lemmas an twelve theorems yielding constraints on system parameters and nonlinearity for asymptotic sta ility in the large and boundedness of solutions of a system of the following three Aizermantype equations: dx = y  f(x), dy = z  x, and dz = ax  bf(x). A method is also advanced for constructing a Lyapunov function for Aizermantype s stems; these Lyap nov functions are of the form: integral of the nonlinearity plus a quadratic form in the state variables. Two of t e twelve theorems yield sufficient conditions for the existence of periodic solutions of the above system; much of the discussion evolves about when satisfaction of the generalized Routh hurwitz implies stability in the large for the n ll solution. No examples or indication towards practical application of the theorems i given. (Author)
Descriptors : *DIFFERENTIAL EQUATIONS, *NONLINEAR DIFFERENTIAL EQUATIONS, FUNCTIONS(MATHEMATICS), INTEGRALS, NONLINEAR SYSTEMS, TRANSLATIONS
Distribution Statement : APPROVED FOR PUBLIC RELEASE