Non-Stationary Oscillations About a Simple Bifurcation

✍ Scribed by H.G. Davies; R. Pan

• Book ID: 102605597
• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 402 KB
• Volume: 172
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1994.1167

✦ Synopsis

The non-stationary response of a non-linear oscillator that exhibits a simple bifurcation from one stable root to another is discussed. The discussion is motivated by previous work on the coupled pitch and role modes of a ship. Two aspects of the analysis are emphasized: (i) aspects of the response described numerically by others are described analytically; and (ii) analysis of the response using only local stability of the two response solutions is inadequate. A global stability criterion is obtained, and it is shown that what appear to be rapid jumps from one solution to another are in fact smooth transitions on the phase plane.