Mathieu's Equation and Its Generalizations: Overview of Stability Charts and Their Features

2018/01/27 by Ivana Kovacic, Ivana Kovačić, Richard Rand +2 · 21 citations
Engineering · Physics and Astronomy · Decision Sciences · #Control Systems and Identification #Quantum chaos and dynamical systems #Scientific Measurement and Uncertainty Evaluation

paper · doi:10.1115/1.4039144

Abstract

This work is concerned with Mathieu's equation—a classical differential equation, which has the form of a linear second-order ordinary differential equation (ODE) with Cosine-type periodic forcing of the stiffness coefficient, and its different generalizations/extensions. These extensions include: the effects of linear viscous damping, geometric nonlinearity, damping nonlinearity, fractional derivative terms, delay terms, quasiperiodic excitation, or elliptic-type excitation. The aim is to provide a systematic overview of the methods to determine the corresponding stability chart, its structure and features, and how it differs from that of the classical Mathieu's equation.

Citations

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