NONLINEAR OSCILLATIONS IN A SECOND ORDER SYSTEM,
Abstract
Relaxation oscillations are investigated. A number of analytic curves are obtained which serve as upper and lower bounds on solution trajectories in this plane. In many cases, piecewise connection of such bounding curves provide annular regions within which periodic orbits lie. The number, location, stability and amplitude bounds of periodic solutions may be determined in this manner. When the method is applied to the equation of van der Pol, the upper and lower bounds obtained for the amplitude of the unique periodic solutions compare favourably with the known asymptotic expansion of the amplitude. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1964
- Accession Number
- AD0433472
Entities
People
- Peter James Ponzo
Organizations
- University of Illinois Urbana–Champaign