Constant-time loci in the phase-plane for nonlinear systems

✍ Scribed by B.L. Deekshatulu; R. Balasubramanian

• Book ID: 103085482
• Publisher: Elsevier Science
• Year: 1965
• Tongue: English
• Weight: 502 KB
• Volume: 280
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(65)90048-7

✦ Synopsis

This paper deals with the term constant time loci (C.T.L.) in the phase-plane and shows that in piecewise linear systems, the isoclines are also the C.T.L. A relation between the slope of the phase trajectory at any point on the phase-plane and the time taken by the system to reach thut point is established, assuming any one of the isoclines as the t = 0 line. As a result, in the case of pieceurise linear systems, time solutions, i.e., x vs. t, can be directly determined from the phase-plane plot. An example demonstrates the e$icacy of this new approach.