A Computer-Simulated Method of Phase-Plane Displacements

[+] Author and Article Information
Louis L. Scharf

Honeywell, Inc., Seattle, Wash.

J. Basic Eng 92(2), 233-237 (Jun 01, 1970) (5 pages) doi:10.1115/1.3424979 History: Received July 29, 1969; Online October 27, 2010


A well-known graphical phase-plane technique for solving a wide variety of ordinary second-order differential equations is shown to satisfy a relatively simple set of iterative relationships which are easily programmed on a digital computer. The only restriction on the differential equation of interest is that it can be written as aẍ + G(x, ẋ, t) = 0, where G(x, ẋ, t) = g(x, ẋ, t) + kx. Consequently, many linear and nonlinear differential equations, with or without forcing functions, which may also have (explicit) time-variable coefficients, are easily solved with the method.

Copyright © 1970 by ASME
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