THE CONSTRUCTION OF PERIODIC SOLUTIONS OF NONLINEAR OSCILLATORS,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1964
- Accession Number
- AD0434453
Entities
People
- J. H. Heinbockel
- Raimond A. Struble
Organizations
- North Carolina State University