Non-Linear Electromechanics

Contents......Page 12
Foreword......Page 6
Introduction......Page 8
1.1 Electrostatics and magnetostatics......Page 16
1.2 The Lagrange-Maxwell equations......Page 23
1.3 Stability of stationary motions of systems with quasi-cyclic coordinates and the mechanical equilibrium under the action of magnetic field......Page 27
1.4 Motion of electromechanical systems due to electromotive forces......Page 38
2.1 Asymptotic transformation of the equations of motion for conducting rigid body in alternating magnetic field......Page 45
2.2 Pendulum in the alternating magnetic field......Page 54
2.3 Magnetic suspension in the field of alternating currents......Page 60
3.1 The idealized model of synchronous machine......Page 78
3.2 Equation of the synchronous machine in the case of a powerful network......Page 80
3.3 Systems with electromagnetic vibration absorbers......Page 92
3.4 Optimal parameters of the magneto-electric extinguisher of small vibrations of a single-degree-of-freedom system......Page 98
3.5 Swinging of the rotor of synchronous machine and motion of the pendulum with magneto-electric extinguishers......Page 103
3.6 Dynamics of synchronous machine that autonomously works on load......Page 112
3.7 Asymptotic transformation of equations when synchronous machine works on load through rectifier......Page 122
3.8 Stationary regimes of operation of rectifier working on pure active load......Page 125
3.9 Control of the load current......Page 131
3.10 Work of generator on counter-electromotive force via rectifier......Page 133
3.11 Control of excitation of brief action turbogenerators......Page 134
3.12 Dynamics of two synchronous generators operating in parallel into a common active-inductive load......Page 143
3.13 Equation for electromechanical processes in inductor machines......Page 158
3.14 Some inverse problems of theory of inductor machines......Page 169
3.15 Single-pack and unlike-pole machines, machines with open slot......Page 170
3.16 Equation of electromechanical processes in three-phase unlikepole machine......Page 174
3.17 Feature of transient processes for star connection with zero wire......Page 183
4.1 Special form of notation for equations of motion and their solutions......Page 187
4.2 Integral stability criterion for periodic motions of electromechanical systems and systems with quasi-cyclic coordinates......Page 194
4.3 Energy relationships for oscillations of current conductors......Page 203
4.4 On the relationship between the resonant and non-resonant solutions......Page 205
4.5 Routh's equations which are linear in the positional coordinates......Page 209
5.1 Equations for determining the constant components of magnetic fluxes......Page 217
5.2 Systems with a single electromagnet......Page 224
5.3 System with electromagnets in the differentiating circuit......Page 232
5.4 Interaction effects. Synthesis of electromagnets for vibration excitation......Page 238
5.5 Generating solution for the induction - field strength nonlinearity......Page 241
5.6 Oscillation of the feed frequency in system with reactive electromagnet......Page 243
5.7 Oscillations in systems with two electromagnets. Asymmetrical modes......Page 248
5.8 Vibrations in system with collisions. Influence of mechanical nonlinearity......Page 253
6.1 Motion due to fast oscillating forces......Page 265
6.2 Motion of the charged particle in high-frequency electromagnetic field......Page 271
6.3 Particle in electromagnetic field with high-frequency and constant components......Page 278
6.4 Relativistic charged particle in essentially heterogeneous crossed electric and magnetic fields......Page 283
6.5 Motion of the non-relativistic particle in heterogeneous magnetic field......Page 292
6.6 Motion of the non-relativistic particle in perturbed axisymmetric field......Page 296
7.1 Statement of "elastic-linear" problems of nonlinear magnetoelasticity......Page 301
7.2 Equilibrium of ferromagnetic bodies. Nonlinear boundary-value problems......Page 306
7.3 Boundary-value problems for equilibrium of conductors with currents......Page 315
7.4 Equilibrium of elastically suspended rigid bodies......Page 320
7.5 Equilibrium of string subjected to magnet force and prescribed external load......Page 323
7.6 The Emden-Fowler equation. Reduction to autonomous system......Page 333
7.7 Equilibrium of ferromagnetic membrane and threads with currents......Page 344
7.8 On the stable equilibrium forms of conductors with currents......Page 348
A.1 Linear equation with coefficients given by asymptotical series......Page 355
A.2 The case when function ξ(τ, ε) is given by an asymptotic sequence......Page 360
A.3 Separating slow variables in quasi-linear systems......Page 362
A.4 Remarks......Page 369
B. Systems integrable in the first approximation of the averaging method......Page 370
C. Higher approximations of the averaging method for systems with discontinuous variables......Page 377
D. On qualitative investigation of motion by the asymptotic methods of nonlinear mechanics......Page 384
References......Page 391
F......Page 402
T......Page 403
Z......Page 404