Skubov Non-Linear Electromechanics

1. Auflage 2008
ISBN: 978-3-540-44779-5
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 399 Seiten

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.

Autoren/Hrsg.

Skubov, Dmitry

Inhaltsverzeichnis

1;Foreword;6
2;Introduction;8
3;Contents;12
4;Description of electromechanical systems;16
4.1;1.1 Electrostatics and magnetostatics;16
4.2;1.2 The Lagrange-Maxwell equations;23
4.3;1.3 Stability of stationary motions of systems with quasi- cyclic coordinates and the mechanical equilibrium under the action of magnetic . eld;27
4.4;1.4 Motion of electromechanical systems due to constant external electromotive forces;38
5;Motion of the conducting rigid body in alternating magnetic . eld;45
5.1;2.1 Asymptotic transformation of the equations of motion for conducting rigid body in alternating magnetic . eld;45
5.2;2.2 Pendulum in the alternating magnetic .eld;54
5.3;2.3 Magnetic suspension in the .eld of alternating currents;60
6;Dynamics of synchronous electric machines;78
6.1;3.1 The idealized model of synchronous machine;78
6.2;3.2 Equation of the synchronous machine in the case of a powerful network;80
6.3;3.3 Systems with electromagnetic vibration absorbers;92
6.4;3.4 Optimal parameters of the magneto-electric extinguisher of small vibrations of a single- degree- of- freedom system;98
6.5;3.5 Swinging of the rotor of synchronous machine and motion of the pendulum with magneto- electric extinguishers;103
6.6;3.6 Dynamics of synchronous machine that autonomously works on load;112
6.7;3.7 Asymptotic transformation of equations when synchronous machine works on load through recti . er;122
6.8;3.8 Stationary regimes of operation of recti.er working on pure active load;125
6.9;3.9 Control of the load current;131
6.10;3.10 Work of generator on counter-electromotive force via recti . er;133
6.11;3.11 Control of excitation of brief action turbogenerators;134
6.12;3.12 Dynamics of two synchronous generators operating in parallel into a common active- inductive load;143
6.13;3.13 Equation for electromechanical processes in inductor machines;158
6.14;3.14 Some inverse problems of theory of inductor machines;169
6.15;3.15 Single-pack and unlike-pole machines, machines with open slot;170
6.16;3.16 Equation of electromechanical processes in three- phase unlike- pole machine;174
6.17;3.17 Feature of transient processes for star connection with zero wire;183
7;Periodic solutions in problems of excitation of mechanical oscillations;187
7.1;4.1 Special form of notation for equations of motion and their solutions;187
7.2;4.2 Integral stability criterion for periodic motions of electromechanical systems and systems with quasi- cyclic coordinates;194
7.3;4.3 Energy relationships for oscillations of current conductors;203
7.4;4.4 On the relationship between the resonant and non- resonant solutions;205
7.5;4.5 Routh’s equations which are linear in the positional coordinates;209
8;Oscillations caused by electromagnets;217
8.1;5.1 Equations for determining the constant components of magnetic . uxes;217
8.2;5.2 Systems with a single electromagnet;224
8.3;5.3 System with electromagnets in the di . erentiating circuit;232
8.4;5.4 Interaction e.ects. Synthesis of electromagnets for vibration excitation;238
8.5;5.5 Generating solution for the induction - .eld strength nonlinearity;241
8.6;5.6 Oscillation of the feed frequency in system with reactive electromagnet;243
8.7;5.7 Oscillations in systems with two electromagnets. Asymmetrical modes;248
8.8;5.8 Vibrations in system with collisions. In.uence of mechanical nonlinearity;253
9;Charged particle in electromagnetic . eld;265
9.1;6.1 Motion due to fast oscillating forces;265
9.2;6.2 Motion of the charged particle in high- frequency electromagnetic .eld;271
9.3;6.3 Particle in electromagnetic .eld with high- frequency and constant components;278
9.4;6.4 Relativistic charged particle in essentially heterogeneous crossed electric and magnetic . elds;283
9.5;6.5 Motion of the non-relativistic particle in heterogeneous magnetic . eld;292
9.6;6.6 Motion of the non-relativistic particle in perturbed axisymmetric . eld;296
10;Some problems of nonlinear magnetoelasticity;301
10.1;7.1 Statement of elastic-linear problems of nonlinear magnetoelasticity;301
10.2;7.2 Equilibrium of ferromagnetic bodies. Nonlinear boundary- value problems;306
10.3;7.3 Boundary-value problems for equilibrium of conductors with currents;315
10.4;7.4 Equilibrium of elastically suspended rigid bodies;320
10.5;7.5 Equilibrium of string subjected to magnet force and prescribed external load;323
10.6;7.6 The Emden-Fowler equation. Reduction to autonomous system;333
10.7;7.7 Equilibrium of ferromagnetic membrane and threads with currents;344
10.8;7.8 On the stable equilibrium forms of conductors with currents;348
11;Averaging quasilinear systems with several fast variables;355
11.1;A.1 Linear equation with coe.cients given by asymptotical series;355
11.2;A.2 The case when function .( t, e) is given by an asymptotic sequence;360
11.3;A.3 Separating slow variables in quasi-linear systems;362
11.4;A.4 Remarks;369
12;Systems integrable in the .rst approximation of the averaging method;370
13;Higher approximations of the averaging method for systems with discontinuous variables;377
14;On qualitative investigation of motion by the asymptotic methods of nonlinear mechanics;384
15;References;391
16;Index;402