Accession Number : AD0434453

Title :   THE CONSTRUCTION OF PERIODIC SOLUTIONS OF NONLINEAR OSCILLATORS,

Corporate Author : NORTH CAROLINA STATE UNIV RALEIGH SCHOOL OF PHYSICAL SCIENCES AND APPLIED MATHEMATICS

Personal Author(s) : Heinbockel,J. H. ; Struble,Raimond A.

Report Date : MAR 1964

Pagination or Media Count : 91

Abstract : Periodic solutions of nonlinear oscillators are investigated using elementary geometrical and analytical arguments. The existence of normal trajectories is established using geometrical arguments and the usual periodicity condition is rephrased so as to permit the use of simple continuity arguments in establishing the periodicity. Some preliminary concepts, as well as a basic theorem and three corollaries concerning the existence of periodic solutions, are introduced. Existence of normal trajectories is discussed. Estimates of elapsed times and the standard existence problem are considered. The general case is discussed and an examination of higher dimensional systems is presented. Certain connections with special concepts which have been employed by other investigators are established. Using these concepts the main results are included in a General Theorem which covers the higher dimensional cases. Throughout the Duffing equation serves as a concrete example. (Author)

Descriptors :   (*OSCILLATORS, NONLINEAR SYSTEMS MACHINES), ELECTRICAL NETWORKS, NONLINEAR DIFFERENTIAL EQUATIONS, DAMPING, VIBRATION

Distribution Statement : APPROVED FOR PUBLIC RELEASE