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Energy-Rate Method

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Approximation Methods in Science and Engineering

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Abstract

Determination of the stability chart and transition curves of parametric differential equations are extremely important in design, optimization, and study of parametric systems. Besides several approximate methods that are capable of determining the stability chart of parametric systems, the energy-rate method is the most exact one. In this chapter we review this analytics-numerical method to determine stable, unstable, and periodic response of differential equations that their stability depends on relation between parameters. We will use the Mathieu equation as the principal example to develop the method.

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Authors and Affiliations

  1. School of Engineering, RMIT University, Melbourne, VIC, Australia

    Reza N. Jazar

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  1. Reza N. Jazar
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N. Jazar, R. (2020). Energy-Rate Method. In: Approximation Methods in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0480-9_6

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