The "dual" state variable (DSV) formulation is a new way to represent ordinary differential equations. It is based on a framework that is consistent with the analysis of linear systems, and it allows the state space representation of a system to exhibit considerable symmetry. Its use in modeling requires a clear understanding of its unique four-dimensional state space, but it can be computationally simple. The DSV formulation has been successfully applied to model the nonlinear pendulum, the Duffing oscillator, and the van der Pol oscillator, with results that are superior to those of perturbation methods. An introduction to the DSV formulation and a framework for its systematic application as a modeling tool for nonlinear oscillators are presented.

Volume Subject Area:
Applied Mechanics
Topics:
Differential equations, Linear systems, Modeling, Pendulums
1.
Post
A.
and
Stuiver
W.
,
2004
, “
Modeling non-linear oscillators: a new approach
,”
Intl. J. of Non-linear Mechanics
,
39
, pp.
897
–
908
.
2.
Post, A. and Stuiver, W., article in press, “A dual state variable model of the van der Pol oscillator,” Intl. J. of Nonlinear Mechanics.
3.
Hagedorn, P., Non-Linear Oscillations. Clarendon Press, Oxford, 1981.
4.
Davis, H., Introduction to Nonlinear Differential and Integral Equations. Dover Publications, New York, 1962 pp354–367.
This content is only available via PDF.
Copyright © 2006
 by ASME
You do not currently have access to this content.