The book comprises a broad panorama of phenomena occurring in four major classes of radiophysical and mechanical systems -- linear, nonlinear, parametric, and nonlinear-parametric. An analytical technique for the broad circle of issues under consideration is developed. It is presented in a user-friendly form, allowing its further direct application in research practices. Analytical methods are presented for investigating modulation-parametric and nonlinear systems, oscillating systems with periodic and almost periodic time-dependent parameters, effects of adaptive self-organization in coupled resonance systems and oscillating systems under the action of external forces, nonlinear with respect to the coordinates of excited systems. Of an interdisciplinary nature, this volume can serve as a handbook for developing lecture courses such as Fundamentals of Nonlinear Dynamics and Theory of Nonlinear Oscillations, Theory of Nonlinear Circuits and Systems, Fundamentals of Radiophysics and Electronics, Theory of Signals and Theoretical Radiophysics, Theoretical Mechanics and Electrodynamics.
Author(s): Vladimir Damgov
Year: 2004
Language: English
Pages: 572
Tags: Математика;Нелинейная динамика;
PREFACE......Page 8
CONTENTS......Page 12
INTRODUCTION......Page 20
1.1. Classification of oscillating systems, which give rise to forces seeking to change the effective reactive parameters…......Page 40
1.2. Generalization of Manley–Row's classical energy relations......Page 42
1.3. Analytical techniques for investigating modulation-parametric phenomena in resonance systems with external pumping......Page 49
1.4. Analytical techniques for investigating modulation-parametric phenomena in generator systems......Page 53
2.1. Methods of controlling the active and reactive parameters in modulation-parametric systems with external pumping......Page 56
2.1.1. Input conductance (impedance) of a cophasal parametric modulator......Page 57
2.1.2. Input admittance (impedance) of a complex parametric modulator with ,,quadratic” pumping of the parametric elements......Page 60
2.1.3. Experimental results concerning the input conductance of a cophasal parametric modulator......Page 61
2.1.4. On the existence of a modulation-parametric channel of energy conversion and input in the course of different…......Page 64
2.2.1. A method for analyzing second order oscillating systems, close to the conservative ones, with strong reactive…......Page 77
2.2.2. Initial model and analytical techniques for investigating perturbed non-autonomous self-oscillating systems......Page 79
2.2.3. Equivalent video-impedance of a one-port represented by an injection-locked oscillator......Page 83
2.2.4. Analysis of the conversion properties of a one-port presented by a non-autonomous oscillator......Page 88
2.2.5. Selective properties of an oscillator with asynchronous action......Page 94
2.3.1. Short-range self-detecting Doppler radars (autodyne systems) described by differential equations of the second order......Page 97
2.3.2. Short-range self-detecting Doppler radar systems described by differential equations of the third order......Page 107
2.4.1. Noise parameters and properties of one-ports with negative parameters built up on the basis of four-frequency…......Page 119
2.4.2. Increasing the sensitivity of receiving systems of the type of a capacitive or inductive video sensor......Page 126
2.4.3. Inductive sensor......Page 127
2.4.4. Capacitive sensor......Page 130
2.4.5. Implementation and utilization of modulation-parametric one-ports with negative conductance (negative resistance)......Page 137
2.4.6. Implementation and utilization of modulation-parametric one-ports with negative capacitance......Page 139
2.4.7. Implementation and utilization of modulation-parametric one-ports with negative inductance......Page 145
2.5. Application of self-oscillating one-ports with controllable parameters......Page 148
3.1. Nonlinear resonance in an oscillating circuit with a p–n junction of a semiconductor diode......Page 157
3.1.1. Effective (equivalent) parameters of the nonlinear oscillating circuit......Page 158
3.1.2. The influence of higher harmonics on nonlinear resonance......Page 161
3.1.3. Numerical analysis of the resonance properties of the oscillating circuit and experimental illustrations......Page 164
3.1.4. Excitation of periodic oscillations on the basis of a nonlinear oscillating circuit with a pronounced hysteretic area…......Page 171
3.2. Nonlinear and parametric resonance in a generalized oscillating circuit......Page 184
3.2.1. Equivalent circuit and approximation of the nonlinear characteristics......Page 185
3.2.2. Equations......Page 187
3.2.3. Forced oscillations......Page 189
3.2.4. Parametric resonance......Page 193
3.3. Generalized modified method of complex amplitudes for analyzing processes in nonlinear oscillating systems......Page 196
3.4. Implementation of parametric one-ports......Page 202
3.5. Influence of the effect of accumulation of a minority carrier charge on the performance of semiconductor diodes in…......Page 213
3.5.1. Phenomenological model of the process of charge accumulation......Page 214
3.5.2. Frequency characteristics of detection......Page 218
3.5.3. Diffusive impedance of the p–n junction at high signal amplitudes and higher frequencies......Page 224
4.1.1. Major concepts: bifurcations, chaos, strange attractor, fractal dimension. Conditions for the manifestation of…......Page 230
4.1.2. Basic mechanisms of transition from determined to chaotic oscillations......Page 235
4.1.3. Methods and criteria for identifying chaotic oscillations......Page 237
4.1.4. Experimental and numerical methods for investigating chaotic oscillations......Page 239
4.2. Chaotic oscillations in non-autonomous radiophysical systems with nonlinear reactance and parametric systems......Page 244
4.3.1. Conditions for chaotization of the oscillations in generator systems......Page 251
4.3.2. Bifurcations and chaos in autonomous and non-autonomous generator systems......Page 253
4.3.3. Creating chaotic oscillations in generator systems with a delayed feedback......Page 257
4.3.4. Chaos in SHF short-range self-detecting Doppler radars......Page 261
5.1. Generalization of the method of complex amplitudes for linear oscillating systems with periodic parameters and…......Page 265
5.2.1. Periodic and almost periodic resistance and conductance......Page 266
5.2.2. Periodic inductance and magnetic susceptibility......Page 273
5.2.3. Periodic capacitance and electric elastance......Page 276
5.2.4. Power consumed by periodic elements of the radio circuits......Page 277
5.3. Nonlinear elements of radiophysical systems......Page 283
5.4. The law of energy conservation in oscillating systems......Page 287
6.1. Free and forced oscillations in a generalized oscillating circuit......Page 291
6.2. Energy balance in a generalized oscillating circuit......Page 297
7.1. Qualitative analysis of the free processes in a generalized linear oscillating circuit with periodic parameters......Page 300
7.1.1. Structure of the differential equations describing linear oscillating systems with positive parameters......Page 301
7.1.2. Vector differential equation describing a linear oscillating circuit with time-dependent parameters......Page 302
7.1.3. Classification of the free processes in Hamiltonian oscillating circuits......Page 308
7.1.4. Phase plane of a linear oscillating circuit with periodic parameters......Page 316
7.1.5. Stability of the canonical systems......Page 319
7.1.6. Stability criteria of a generalized linear resonance circuit......Page 324
7.1.7. Stability of an oscillating circuit with a piece-wise linear volt-coulomb characteristic......Page 330
7.1.8. Analysis of the free processes in a linear quasi-harmonic oscillating circuit......Page 333
7.2. Stationary regime in linear radiophysical systems with periodic and almost periodic parameters......Page 336
7.3. Parametric resonance in a linear oscillating circuit with periodic parameters......Page 347
7.3.1. Resonance 1. Geometric meaning of the resonance in a linear oscillating circuit with periodic parameters......Page 348
7.3.2. Resonance 2. First and second power resonance of a linear oscillating circuit with periodic parameters......Page 355
7.3.3. Resonance 3. Equation of the natural oscillations in the instability range......Page 359
8.1. The principle of linear connection in the analysis of forced oscillations in a nonlinear oscillating circuit......Page 367
8.2. ,,Strong” and ,,weak” resonance in a nonlinear system with explicitly time-dependent parameters......Page 376
8.3. Quasi-periodic oscillations in an auto-generator with an oscillating circuit containing nonlinear reactance......Page 383
8.4. Thermoparametric oscillations......Page 386
9.1. Introduction......Page 391
9.2. Generalized conditions for grouping in stable electromechanical formations......Page 393
9.3. Peculiarities of the processes of interaction between coupled oscillating systems......Page 396
9.4. Electromagnetic tracking system......Page 399
9.5.1. Conditions for grouping two oscillating systems with changing capacitive and constant ohmic coupling in stable…......Page 401
9.5.2. Ponderomotive forces and interaction energy in connected resonance systems with self-tuning capacitance......Page 403
9.6. Grouping of coupled dipole resonators under the action of an external electromagnetic wave......Page 405
10.1. Introduction (Major model notions)......Page 410
10.2. Numerical experiment of excitation of ,,quantized” pendulum oscillations......Page 417
10.3.1. An approach used in the case of small amplitudes of pendulum oscillation......Page 438
10.3.2. Spectrum of the possible oscillation amplitudes of a pendulum under the action of an external nonhomogeneous force......Page 444
10.3.3. Rotator under non-homogeneous action......Page 454
10.3.4. General conditions for pendulum oscillation excitation under the action of an external nonlinear force......Page 458
10.3.5. A proof of the existence of a modulation – parametric channel for energy input in the oscillation process......Page 464
10.3.6. Excitation of continuous oscillations with a discrete set of stable amplitudes in a pseudo-linear oscillating system......Page 469
10.3.7. Pendulum oscillations in case of oddness of the external exciting force......Page 480
10.3.8. Approach in case of large amplitudes of pendulum oscillation......Page 483
10.4.1. A model of the interaction of an oscillator with an electromagnetic wave: an approach in the case of small…......Page 491
10.4.2. ,,Quantized“ cyclotron motion......Page 494
10.4.3. The wave nature and dynamical quantization of the Solar System......Page 502
10.4.4. Approach in the case of large amplitudes of the oscillations in a nonlinear dynamical system existing under wave…......Page 510
10.4.5. General conditions for transition to irregular behavior in an oscillator under wave action......Page 513
10.5.1. Energy balance of the system......Page 516
10.5.2. Construction of a discrete map......Page 517
10.5.3. Fixed stationary map points......Page 519
10.5.4. Stability of the stationary points. Conditions for bifurcation doubling of period......Page 521
10.5.5. Generation of complex periodic solutions: multiplications in weakly dissipative maps......Page 523
10.5.6. On the class of radial twist maps......Page 526
10.5.7. Twist Maps and Hamiltonian Dynamics......Page 530
10.5.8. Generalized Dissipative Twist Map of the Class of Kick-Excited Self-Adaptive Systems......Page 533
10.6. General Characteristics of the Class of Kick-Excited Self-Adaptive Dynamical Systems. Conclusions......Page 536
CONCLUSION......Page 543
REFERENCES......Page 550
SUBJECT INDEX......Page 567
