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Cover image for Non-linear electromechanics
Title:
Non-linear electromechanics
Personal Author:
Series:
Foundations of engineering mechanics
Publication Information:
Berlin : Springer, 2008
Physical Description:
xiv, 397 p. : ill. ; 24 cm.
ISBN:
9783540251392

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30000010193850 TK2000 S58 2008 Open Access Book Book
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Summary

Summary

This is the first book in which problems of electromechanics are considered from the perspective of analytical mechanics. The book includes fundamental results in the theory of non-linear electromechanical systems and will useful both for researches, engineers, scholars and graduate students of electromechanical faculties of technical universities. It includes not only theoretical results but also various examples from many industrial applications. A sizeable part of the book is devoted to the general theory of synchronous machines and electro-magnetic exciters of oscillations. The material of the book can be included in courses covering the theory of non-linear oscillations, the theory of electrical machines and other electromechanical devices.


Table of Contents

Forewordp. v
Introductionp. vii
1 Description of electromechanical systemsp. 1
1.1 Electrostatics and magnetostaticsp. 1
1.2 The Lagrange-Maxwell equationsp. 8
1.3 Stability of stationary motions of systems with quasi-cyclic coordinates and the mechanical equilibrium under the action of magnetic fieldp. 12
1.4 Motion of electromechanical systems due to electromotive forcesp. 23
2 Motion of the conducting rigid body in alternating magnetic fieldp. 31
2.1 Asymptotic transformation of the equations of motion for conducting rigid body in alternating magnetic fieldp. 31
2.2 Pendulum in the alternating magnetic fieldp. 40
2.3 Magnetic suspension in the field of alternating currentsp. 46
3 Dynamics of synchronous electric machinesp. 65
3.1 The idealized model of synchronous machinep. 65
3.2 Equation of the synchronous machine in the case of a powerful networkp. 67
3.3 Systems with electromagnetic vibration absorbersp. 79
3.4 Optimal parameters of the magneto-electric extinguisher of small vibrations of a single-degree-of-freedom systemp. 85
3.5 Swinging of the rotor of synchronous machine and motion of the pendulum with magneto-electric extinguishersp. 90
3.6 Dynamics of synchronous machine that autonomously works on loadp. 99
3.7 Asymptotic transformation of equations when synchronous machine works on load through rectifierp. 109
3.8 Stationary regimes of operation of rectifier working on pure active loadp. 112
3.9 Control of the load currentp. 118
3.10 Work of generator on counter-electromotive force via rectifierp. 120
3.11 Control of excitation of brief action turbogeneratorsp. 121
3.12 Dynamics of two synchronous generators operating in parallel into a common active-inductive loadp. 130
3.13 Equation for electromechanical processes in inductor machinesp. 145
3.14 Some inverse problems of theory of inductor machinesp. 156
3.15 Single-pack and unlike-pole machines, machines with open slotp. 157
3.16 Equation of electromechanical processes in three-phase unlike-pole machinep. 161
3.17 Feature of transient processes for star connection with zero wirep. 170
4 Periodic solutions in problems of excitation of mechanical oscillationsp. 175
4.1 Special form of notation for equations of motion and their solutionsp. 175
4.2 Integral stability criterion for periodic motions of electromechanical systems and systems with quasi-cyclic coordinatesp. 182
4.3 Energy relationships for oscillations of current conductorsp. 191
4.4 On the relationship between the resonant and non-resonant solutionsp. 193
4.5 Routh's equations which are linear in the positional coordinatesp. 197
5 Oscillations caused by electromagnetsp. 205
5.1 Equations for determining the constant components of magnetic fluxesp. 205
5.2 Systems with a single electromagnetp. 212
5.3 System with electromagnets in the differentiating circuitp. 220
5.4 Interaction effects. Synthesis of electromagnets for vibration excitationp. 226
5.5 Generating solution for the induction - field strength nonlinearityp. 229
5.6 Oscillation of the feed frequency in system with reactive electromagnetp. 231
5.7 Oscillations in systems with two electromagnets. Asymmetrical modesp. 236
5.8 Vibrations in system with collisions. Influence of mechanical nonlinearityp. 241
6 Charged particle in electromagnetic fieldp. 253
6.1 Motion due to fast oscillating forcesp. 253
6.2 Motion of the charged particle in high-frequency electromagnetic fieldp. 259
6.3 Particle in electromagnetic field with high-frequency and constant componentsp. 266
6.4 Relativistic charged particle in essentially heterogeneous crossed electric and magnetic fieldsp. 271
6.5 Motion of the non-relativistic particle in heterogeneous magnetic fieldp. 280
6.6 Motion of the non-relativistic particle in perturbed axisymmetric fieldp. 284
7 Some problems of nonlinear magnetoelasticityp. 289
7.1 Statement of "elastic-linear" problems of nonlinear magnetoelasticityp. 289
7.2 Equilibrium of ferromagnetic bodies. Nonlinear boundary-value problemsp. 294
7.3 Boundary-value problems for equilibrium of conductors with currentsp. 303
7.4 Equilibrium of elastically suspended rigid bodiesp. 308
7.5 Equilibrium of string subjected to magnet force and prescribed external loadp. 311
7.6 The Emden-Fowler equation. Reduction to autonomous systemp. 321
7.7 Equilibrium of ferromagnetic membrane and threads with currentsp. 332
7.8 On the stable equilibrium forms of conductors with currentsp. 336
Appendicesp. 343
A Averaging quasilinear systems with several fast variablesp. 343
A.1 Linear equation with coefficients given by asymptotical seriesp. 343
A.2 The case when function [xi]([tau], [epsilon]) is given by an asymptotic sequencep. 348
A.3 Separating slow variables in quasi-linear systemsp. 350
A.4 Remarksp. 357
B Systems integrable in the first approximation of the averaging methodp. 359
C Higher approximations of the averaging method for systems with discontinuous variablesp. 367
D On qualitative investigation of motion by the asymptotic methods of nonlinear mechanicsp. 375
Referencesp. 383
Indexp. 395
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