Analogy of nonlinear systems to classical dynamics

✍ Scribed by Ruey-Wen Liu; Gilbert H. Fett

• Publisher: Elsevier Science
• Year: 1961
• Tongue: English
• Weight: 620 KB
• Volume: 272
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(61)90561-0

✦ Synopsis

The two-dimensional autonomous system in the geueral form is considered. The solution is in terms of the phase trajectories in the phase plane. In this paper, a force field over the phase plane is formulated such that the path of a particle in this force field coincides with the path of the trajectories, provided the initial condition is properly chosen. Hence, the trajectories can be obtained by solving the path of the particle subject to the formulated force field. It is further developed that, for any given system, it is theoretically possible to formulate a conservative force field to give the same property. Consequently, it is found out that the trajectories can be solved either analytically by a simple substitution or graphically by means of the family of trajectories which are orthogonal to the trajectories of the original system. Various examples including the generalized Van der Pol equation are given gs illustrations.