Accession Number : AD0732212

Title :   A Study of Weakly Nonlinear Dynamical Systems and Their Stability.

Descriptive Note : Final scientific rept. 16 Sep 65-15 Aug 71,

Corporate Author : MINNESOTA UNIV MINNEAPOLIS DEPT OF AEROSPACE ENGINEERING AND MECHANICS

Personal Author(s) : Sethna,P. R.

Report Date : NOV 1971

Pagination or Media Count : 11

Abstract : The research results are concentrated in four major areas. The first concerns the local behavior of dynamical systems, in particular nonautonomous systems represented by systems of ordinary differential equations almost periodic in time and dependent on a parameter. The main results concern methods for obtaining approximations to solutions that approach stable almost periodic solutions as time goes to infinity. The second concerns systems dependent on fast and slow time, in particular asymptotic results valid for all time for such systems. The results are applied to obtain physically important results for dynamical systems with parametric excitation of high frequency. The third concerns a new approach to the method of averaging, in particular a generalization applicable to a broader class of systems. The basic approach employs arguments related to Liapunov converse theorems. The fourth concerns gyroscopic systems with high spin gyroscopes, in particular results valid for finite intervals of time, and results pertaining to periodic solutions of high spin gyroscopic systems. (Author)

Descriptors :   (*CONTROL SYSTEMS, MATHEMATICAL MODELS), DIFFERENTIAL EQUATIONS, ASYMPTOTIC SERIES, NONLINEAR SYSTEMS, STABILITY, GYROSCOPES, OSCILLATION, PERTURBATION THEORY

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE