Accession Number : AD0662739

Title :   RESONANCE IN ALMOST LINEAR SYSTEMS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Levey,H. C. ; Mahony,J. J.

Report Date : AUG 1967

Pagination or Media Count : 32

Abstract : Estimates, useful for all times, are sought for the resonant response of a system with small non-linearity. It is shown that the method of multiple scales can be used to generate a representation which is formally asymptotic at all times and over a significant time interval is a valid approximation to some solution of the system. It is shown, by example that this estimate is not always a useful representation of any one solution for all time. Plausible arguments are given that the approximation is nevertheless useful for the determination of the behavior of a physical system if not of the pathological solutions of the differential equations which may represent it. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, RESONANCE), (*RESONANCE, LINEAR SYSTEMS), PERIODIC VARIATIONS, RESPONSE, APPROXIMATION(MATHEMATICS), OSCILLATION, TRANSCENDENTAL FUNCTIONS, PROBLEM SOLVING

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE