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.
The Dual State Variable Formulation as an Alternative to Perturbation Methods for the Analysis of Non-Linear Oscillators
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Post, A, & Stuiver, W. "The Dual State Variable Formulation as an Alternative to Perturbation Methods for the Analysis of Non-Linear Oscillators." Proceedings of the ASME 2006 International Mechanical Engineering Congress and Exposition. Applied Mechanics. Chicago, Illinois, USA. November 5–10, 2006. pp. 367-371. ASME. https://doi.org/10.1115/IMECE2006-14534
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