## Nonlinear system analysis |

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### Contents

Linearity and Nonlinearity | 1 |

Approximate Solutions of the Pendulum Equation | 7 |

Exact Solution by Elliptic Integral | 18 |

Copyright | |

36 other sections not shown

### Common terms and phrases

Accordingly amplitude a0 angular frequency applied assume assumption axis betatron betatron oscillations Blaquière Campbell's theorem Chapter coefficient components computed condition constant corresponding coupling damping deduce defined describing function determined deviation diagram differential equation discussion domain easily equation of motion equiamplitude curve equifrequency curves equipotential curve example first-order approximation fluctuations forcing function formula given Grivet harmonic hodograph impulses input integral curve interval introduced line width linear system maser Mathieu equation matrix matter of fact neighborhood noise Nonlinear Oscillations nonlinear systems obtained output parameter particle pendulum periodic periodic function perturbation phase plane problem pulses replaced representation resonance respect rewritten right side saddle point Section separatrix shown in Fig signal singular points sinusoidal slowly varying functions stability stationary steady motion stroboscopic substituting sufficiently small superposition principle synchronized solution tangent tank circuit term theory trajectory transformation tube unstable variables vector viewpoint