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Analytical Methods for Solving Nonlinear Differential Equations
Graphical Methods for Solving Nonlinear Differential Equations
Subharmonic Oscillations of Order One Half
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1/2-harmonic oscillations 1/2-harmonic response amplitude amplitude and phase analog-computer analysis analytical methods Appendix Approximate Solution attraction leading axis chapter constant cosr curves of Eq delta method described determined differing in phase directly unstable domains of attraction Duffing's equation external force Fourier series frequency graphical construction graphical methods harmonic balance harmonic oscillation harmonic response initial conditions lead initial point integral curves iteration method Kyoto University Lienard's method limit cycle linear linear simultaneous equations method of harmonic nonlinear differential equations Numerical Example Order of Approximation oscillations of order period 2k periodic solution Eq perturbation method plane procedure radians representative point right-hand side saddle point Saddle unstable second approximation second-order Section 3.3 side of Eq singular points slopeline method small parameter solution curve solution of Duffing's solution of Eq solving nonlinear differential Stable focus stable singularities subharmonic oscillations subharmonic response Substituting Eq system parameters terms of order unknown quantities unstable fixed point variables