Phase Trajectory Construction of High-Order, Nonlinear, Time-Varying, Nonautonomous Systems

[+] Author and Article Information
G. C. Reis

Department of Electrical Engineering, Drexel Institute of Technology, Philadelphia, Pa.

J. Basic Eng 88(2), 311-315 (Jun 01, 1966) (5 pages) doi:10.1115/1.3645852 History: Received April 08, 1964; Online November 03, 2011


A graphical procedure for constructing the time response of a system from its phase-plane trajectory is described. From this, a graphical solution of the equation ẍ + θ(ẋ)g(x) + φ(ẋ) + h(x) = F(t) is presented. The construction procedure for the equation ẍ + φ(ẋ) + c(t)X(x) = F(t) is detailed as a special case of the more general form

ẍ + a(t)M(x)N(ẋ) + θ(ẋ)g(x) + b(t)Q(ẋ)
   + φ(ẋ) + c(t)X(x) + h(x) = F(t)
which can also be solved in a similar fashion. The extension of these techniques to higher-order systems is presented.

Copyright © 1966 by ASME
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