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[资源] 牛津----非线性普通微分方程--第4版--Nonlinear Ordinary Differential Equation

1 Second-order differential equations in the phase plane 1
1.1 Phase diagram for the pendulum equation 1
1.2 Autonomous equations in the phase plane 5
1.3 Mechanical analogy for the conservative system¨x = f(x) 14
1.4 The damped linear oscillator 21
1.5 Nonlinear damping: limit cycles 25
1.6 Some applications 32
1.7 Parameter-dependent conservative systems 37
1.8 Graphical representation of solutions 40
Problems 42

2 Plane autonomous systems and linearization

4 Periodic solutions; averaging methods 125
4.1 An energy-balance method for limit cycles 125
4.2 Amplitude and frequency estimates: polar coordinates 130
4.3 An averaging method for spiral phase paths 134
4.4 Periodic solutions: harmonic balance 138
4.5 The equivalent linear equation by harmonic balance 140
Problems 143

5 Perturbation methods 149
5.1 Nonautonomous systems: forced oscillations 149
5.2 The direct perturbation method for the undamped Duffing’s equation 153
5.3 Forced oscillations far from resonance 155
5.4 Forced oscillations near resonance with weak excitation 157
5.5 The amplitude equation for the undamped pendulum 159
5.6 The amplitude equation for a damped pendulum 163
5.7 Soft and hard springs 164
5.8 Amplitude–phase perturbation for the pendulum equation 167
5.9 Periodic solutions of autonomous equations (Lindstedt’s method) 169
5.10 Forced oscillation of a self-excited equation 171
5.11 The perturbation method and Fourier series 173
5.12 Homoclinic bifurcation: an example 175
Problems 179

8 Stability 259
8.1 Poincaré stability (stability of paths) 260
8.2 Paths and solution curves for general systems 265
8.3 Stability of time solutions: Liapunov stability 267
8.4 Liapunov stability of plane autonomous linear systems 271
8.5 Structure of the solutions ofn-dimensional linear systems 274
8.6 Structure ofn-dimensional inhomogeneous linear systems 279
8.7 Stability and boundedness for linear systems 283
8.8 Stability of linear systems with constant coefficients 284
8.9 Linear approximation at equilibrium points for first-order systems in n variables 289
8.10 Stability of a class of non-autonomous linear systems inn dimensions 293
8.11 Stability of the zero solutions of nearly linear systems 298
Problems 300

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附件 1 : diff_equation.pdf

2015-04-13 16:53:21, 6.21 M

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