Author(s): W J Cunningham
Publisher: MGH
Year: 1958
Language: English
Pages: 357
Title Page......Page 1
Copyright......Page 2
Preface......Page 4
Contents......Page 6
1. Introduction......Page 9
2.1 Introduction......Page 16
2.2 Use of Taylor's Series......Page 18
2.3 Modified Euler Method......Page 20
2.4 Adams Method......Page 22
2.5 Checking Procedures......Page 25
2.6 Equations of Order Higher than First......Page 31
2.7 Summary......Page 34
3.2 Isocline Method, First-order Equation......Page 36
3.3 Isocline Method, Second-order Equation. Phase-plane Diagram......Page 40
3.4 Time Scale on the Phase Plane......Page 44
3.5 Delta Method, Second-order Equation......Page 47
3.6 Lienard Method......Page 52
3.7 Change of Variable......Page 53
3.8 Graphical Integration......Page 56
3.9 Preisman Method......Page 57
3.10 Summary......Page 61
4.2 Specific Types of Equations......Page 63
4.3 Variation of Parameters......Page 71
4.4 Equations Linear in Segments......Page 74
4.5 Equations Leading to Elliptic Functions......Page 82
4.6 Properties of Elliptic Functions......Page 87
4.7 Summary......Page 92
5.2 Type of Equation under Investigation......Page 93
5.3 Linear Transformations......Page 94
5.4 Equations in Normal Form......Page 98
5.5 Types of Singularities......Page 101
5.6 Sketching of Solution Curves......Page 107
5.7 Forcing Functions as Steps or Ramps......Page 111
5.8 Analysis Combining Singularities and Linear Segments......Page 114
5.9 Potential Energy of Conservative Systems......Page 122
5.10 Summary......Page 127
6.1 Introduction......Page 129
6.2 Perturbation Method......Page 131
6.3 Reversion Method......Page 141
6.4 Variation of Parameters......Page 143
6.5 Use of Several Methods......Page 148
6.6 Averaging Methods Based on Residuals......Page 159
6.7 Principle of Harmonic Balance......Page 172
6.8 Summary......Page 177
7.1 Introduction......Page 179
7.2 Principle of Harmonic Balance......Page 180
7.3 Iteration Procedure......Page 196
7.4 Perturbation Method......Page 197
7.5 Extension of Concepts from Linear Systems......Page 208
7.6 Forced Oscillation in a Self- oscillatory System......Page 221
7.7 Summary......Page 228
8.1 Introduction......Page 229
8.2 Linear Difference Equations......Page 230
8.3 Linear Differential-difference Equation......Page 234
8.4 Nonlinear Difference Equation......Page 238
8.5 Nonlinear Differential-difference Equations......Page 241
8.6 Graphical Solutions......Page 246
8.7 Summary......Page 251
9.1 Introduction......Page 253
9.2 First-order Equation......Page 254
9.3 Second-order Equation......Page 258
9.4 Mathieu Equation......Page 267
9.5. Summary.......Page 288
10.2 Structural Stability......Page 289
10.3 Dynamical Stability......Page 290
10.4 Test for Stability of System with Nonoscillatory Steady State......Page 293
10.5 Test for Stability of Oscillating Systems......Page 303
10.6 Stability of Feedback Systems......Page 309
10.7 Orbital Stability of Self-oscillating Systems......Page 317
10.8 Orbital Stability with Two Components......Page 320
10.9 Summary......Page 327
Problems......Page 329
Bibliography......Page 345
Index......Page 353
