Non-Linear Electromechanics

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Springer Science & Business Media, Aug 15, 2008 - Technology & Engineering - 399 pages
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This is the first book to view problems of electromechanics through the lens of analytical mechanics. It offers fundamental results in the theory of non-linear electromechanical systems and includes examples of industrial applications.

 

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Contents

Description of electromechanical systems
1
12 The LagrangeMaxwell equations
8
13 Stability of stationary motions of systems with quasicyclic coordinates and the mechanical equilibrium under the action of magnetic field
12
14 Motion of electromechanical systems due to constant external electromotive forces
23
Motion of the conducting rigid body in alternating magnetic field
31
22 Pendulum in the alternating magnetic field
40
23 Magnetic suspension in the field of alternating currents
46
Dynamics of synchronous electric machines
64
53 System with electromagnets in the differentiating circuit
220
54 Interaction effects Synthesis of electromagnets for vibration excitation
226
55 Generating solution for the induction field strength nonlinearity
229
56 Oscillation of the feed frequency in system with reactive electromagnet
231
electromagnets Asymmetrical modes
236
58 Vibrations in system with collisions Influence of mechanical nonlinearity
241
Charged particle in electromagnetic field
253
62 Motion of the charged particle in highfrequency electromagnetic field
259

32 Equation of the synchronous machine in the case of a powerful network
67
33 Systems with electromagnetic vibration absorbers
79
34 Optimal parameters of the magnetoelectric extinguisher of small vibrations of a singledegreeoffreedom system
85
35 Swinging of the rotor of synchronous machine and motion of the pendulum with magnetoelectric extinguishers
90
36 Dynamics of synchronous machine that autonomously works on load
99
37 Asymptotic transformation of equations when synchronous machine works on load through rectifier
109
38 Stationary regimes of operation of rectifier working on pure active load
112
39 Control of the load current
118
310 Work of generator on counterelectromotive force via rectifier
120
311 Control of excitation of brief action turbogenerators
121
312 Dynamics of two synchronous generators operating in parallel into a common activeinductive load
130
313 Equation for electromechanical processes in inductor machines
145
314 Some inverse problems of theory of inductor machines
156
315 Singlepack and unlikepole machines machines with open slot
157
316 Equation of electromechanical processes in threephase unlikepole machine
161
317 Feature of transient processes for star connection with zero wire
170
Periodic solutions in problems of excitation of mechanical oscillations
175
42 Integral stability criterion for periodic motions of electromechanical systems and systems with quasicyclic coordinates
182
43 Energy relationships for oscillations of current conductors 191
191
44 On the relationship between the resonant and nonresonant solutions
193
45 Rouths equations which are linear in the positional coordinates
197
Oscillations caused by electromagnets
205
52 Systems with a single electromagnet
212
highfrequency and constant components
266
64 Relativistic charged particle in essentially heterogeneous crossed electric and magnetic fields
271
65 Motion of the nonrelativistic particle in heterogeneous magnetic field
280
66 Motion of the nonrelativistic particle in perturbed axisymmetric field
284
Some problems of nonlinear magnetoelasticity
289
72 Equilibrium of ferromagnetic bodies Nonlinear boundaryvalue problems
294
73 Boundaryvalue problems for equilibrium of conductors with currents
303
74 Equilibrium of elastically suspended rigid bodies
308
75 Equilibrium of string subjected to magnet force and prescribed external load
311
76 The EmdenFowler equation Reduction to autonomous system
321
77 Equilibrium of ferromagnetic membrane and threads with currents
332
78 On the stable equilibrium forms of conductors with currents
336
Averaging quasilinear systems with several fast variables
343
A2 The case when function ξτεisgivenbyan asymptotic sequence
348
A3 Separating slow variables in quasilinear systems
350
A4 Remarks
357
Systems integrable in the first approximation of the averaging method
358
Higher approximations of the averaging method for systems with discontinuous variables
367
On qualitative investigation of motion by the asymptotic methods of nonlinear mechanics
374
References
383
Index
394
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