Analysis of Periodically Time-Varying Systems

摘要: Part-I Theory and Techniques.- 1 Historical Perspective.- 1.1 The Nature of Systems with Periodically Time-Varying Parameters.- 1.2 1831-1887 Faraday to Rayleigh-Early Experimentalists Theorists.- 1.3 1918-1940 First Applications.- 1.4 Second Generation 1.5 Recent Theoretical Developments.- 1.6 Commonplace Illustrations Parametric Behaviour.- References for Chapter 1.- Problems.- 2 Equations Their Properties.- 2.1 Hill Equations.- 2.2 Matrix Formulation 2.3 State Transition Matrix.- 2.4 Floquet Theory.- 2.5 Order Systems.- 2.6 Natural Modes Solution.- 2.7 Concluding Comments.- 2.- 3 Solutions Periodic Differential 3.1 Over One Period the Coefficient.- 3.2 Meissner Equation.- 3.3 Solution at Any Time a 3.4 Evaluation ?(?, 0)m, m Integral.- 3.5 Equation Staircase 3.6 Sawtooth Waveform 3.6.1 Wronskian z Negative.- 3.6.2 Zero.- 3.6.3 Case ? 3.7 Positive Slope, 3.8 Triangular 3.9 Trapezoidal 3.10 Bessel Function Generation.- 3.11 Repetitive Exponential 3.12 Coefficient in Form Sequence Impulses.- 3.13 Higher Order.- 3.14 Response Sinusoidal Forcing Function.- 3.15 Phase Space Analysis.- 3.16 3.- 4 Stability.- 4.1 Types 4.2 Stability Theorems 4.3 4.3.1 Characteristic Exponent.- 4.3.2 4.3.3 an Impulsive 4.3.4 4.3.5 4.3.6 Determinant 4.3.7 Frequencies 4.4 General 4.4.1 Analysis 4.4.2 Residues q 0.- 4.4.3 Instability 4.4.4 Diagrams 4.5 Mode Diagrams.- 4.5.1 Basis Solutions.- 4.5.2 P Type 4.5.3 C 4.5.4 N 4.5.5 4.5.6 System.- 4.5.7 Boundary Modes.- 4.5.8 System Losses.- 4.5.9 4.5.10 Coexistence.- 4.6 Short 4.- 5 A Modelling Technique 5.1 Convergence Significance Harmonics Coefficients.- 5.1.1 5.1.2 5.2 Philosophy Intractable 5.3 Frequency Spectrum 5.4 Piecewise Linear Models.- 5.4.1 5.4.2 5.5 Forced Modelling.- 5.6 Diagram Exponent 5.7 Models Nonlinear 5.8 Note on Discrete Spectral 5.9 Remarks.- 5.- 6 Mathieu 6.1 Classical Methods Limitations.- 6.1.1 6.1.2 Functions Fractional 6.1.3 Unstable 6.1.4 Limitations Method Treatment.- 6.2 Numerical 6.3 Techniques 6.3.1 Rectangular 6.3.2 6.3.3 6.3.4 Performance Comparison 6.4 6.4.1 Lossless 6.4.2 Damped (Lossy) 6.4.3 Sufficient Conditions 6.- II 7 Practical Variable 7.1 Quadrupole Mass Spectrometer.- 7.1.1 Spatially Electric Fields.- 7.1.2 Filter.- 7.1.3 Monopole 7.1.4 Ion Trap.- 7.1.5 Simulation Devices.- 7.1.6 Non idealities 7.2 Dynamic Buckling Structures.- 7.3 Elliptical Waveguides.- 7.3.1 Helmholtz 7.3.2 7.3.3 Circular 7.3.4 7.3.5 Computation Cut-off Waveguide..- 7.4 Wave Propagation Media.- 7.4.1 Pass Stop Bands.- 7.4.2 - ?r (Brillouin) Diagram.- 7.4.3 Electromagnetic 7.4.4 Guided 7.4.5 Electrons Crystal Lattices.- 7.4.6 Other Examples Waves Media:.- 7.5 Circuit 7.5.1 Degenerate Amplification.- 7.5.2 Amplification High Networks.- 7.5.3 Nondegenerate 7.5.4 Up Converters.- 7.5.5 N-path 7.- Appendix by Chebyshev Polynomial Methods.- Appendix.