Dynamics of Synchronising Systems

This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretatio...

Full description

Main Author: Nagaev, R.F.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2003, 2003
Edition:1st ed. 2003
Series:Foundations of Engineering Mechanics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
LEADER 07382nmm a2200493 u 4500
001 EB000656756
003 EBX01000000000000000509838
005 00000000000000.0
007 cr|||||||||||||||||||||
008 140122 ||| eng
020 |a 9783540457619 
100 1 |a Nagaev, R.F. 
245 0 0 |a Dynamics of Synchronising Systems  |h Elektronische Ressource  |c by R.F. Nagaev 
250 |a 1st ed. 2003 
260 |a Berlin, Heidelberg  |b Springer Berlin Heidelberg  |c 2003, 2003 
300 |a X, 326 p. 22 illus  |b online resource 
505 0 |a 1 Locally integrable dynamical systems -- 1.1 Concept of local integrability -- 1.2 Linear heterogeneous systems -- 1.3 Piecewise-continuous systems -- 1.4 Homogeneous Lyapunov systems -- 1.5 On local integrability of the equations of motion of Hess’s gyro -- 2 Conservative dynamical systems -- 2.1 Introductory remarks -- 2.2 Conservative mechanical systems -- 2.3 Generalised Jacobi integral -- 2.4 Conservative system in the presence of the generalised gyroscopic forces -- 2.5 Electromechanical systems -- 2.6 Planar systems which admit the first integral -- 3 Dynamical systems in a plane -- 3.1 Conservative systems in a plane -- 3.2 Libration in the conservative system with a single degree of freedom -- 3.3 Rotational motion of the conservative system with one degree of freedom -- 3.4 Backbone curve and its steepness coefficient -- 3.5 Dynamical system with an invariant relationship -- 3.6 Canonisation of a system about the equilibrium position --  
505 0 |a 3.7 Canonised form of the equations of motion -- 4 Conservative systems with many degrees of freedom -- 4.1 Action-angle variables -- 4.2 Conservative systems moving by inertia -- 4.3 The problem of spherical motion of a free rigid body (Euler’s case) -- 4.4 On degeneration of integrable conservative systems -- 4.5 Conservative systems with a single positional coordinate -- 4.6 Motion of an elastically mounted, unbalanced rotor -- 4.7 Spherical motion of an axisymmetric heavy top -- 4.8 Selecting the canonical action-angle variables -- 4.9 Nearly recurrent conservative systems -- 5 Resonant solutions for systems integrable in generating approximation -- 5.1 Introductory remarks -- 5.2 On transition to the angle-action variables -- 5.3 Excluding non-critical fast variables -- 5.4 Averaging equations of motion in the vicinity of the chosen torus -- 5.5 Existence and stability of stationary solution of the averaged system --  
505 0 |a 9.3 Stability of the synchronous-synphase regime -- 9.4 Self-synchronisation of vibration exciters of anharmonic forces of the constant direction -- 9.5 Stabilisation of the working synchronous regime -- 9.6 Two vibration exciters mounted on the carrying system of vibroimpact type -- 10 Synchronisation of dynamical objects of the general type -- 10.1 Weak interaction of anisochronous and isochronous objects -- 10.2 Synchronisation of the quasi-conservative objects with several degrees of freedom -- 10.3 Non-quasiconservative theory of synchronisation -- 10.4 On the influence of friction in the carrying system on the stability of synchronous motion -- 11 Periodic solutions in problems of excitation of mechanical oscillations -- 11.1 Special form of notation for equations of motion and their solutions -- 11.2 Integral stability criterion for periodic motions of electromechanical systems and systems with quasi-cyclic coordinates --  
505 0 |a 11.3 Energy relationships for oscillations of current conductors -- 11.4 On the relationship between the resonant and non-resonant solutions -- 11.5 Routh’s equations which are linear in the positional coordinates -- References 
505 0 |a 5.6 Existence and stability of “partially-autonomous” tori -- 5.7 Anisochronous and quasi-static criteria of stability of a single frequency regime -- 5.8 Periodic solutions of the piecewise continuous systems -- 6 Canonical averaging of the equations of quantum mechanics -- 6.1 Introductory remarks -- 6.2 Stationary Schrödinger’s equation as a classical Hamiltonian system -- 6.3 General properties of the canonical form of Schrödinger’s equation -- 6.4 Stationary perturbation of a non-degenerate level of the discrete spectrum -- 6.5 Stationary excitation of two close levels -- 6.6 Non-stationary Schrödinger’s equation as a Hamiltonian system -- 6.7 Adiabatic approximation -- 6.8 Post-adiabatic approximation -- 6.9 Quantum linear oscillator in a variable homogeneous field -- 6.10 Charged linear oscillator in an adiabatic homogeneous field -- 6.11 Adiabatic perturbation theory -- 6.12 Harmonic excitation of a charged oscillator. Non-resonant case --  
505 0 |a 6.13 Harmonic excitation of an oscillator. Transition through a resonance -- 7 The problem of weak interaction of dynamical objects -- 7.1 The types of conservative interaction and criteria of their weakness -- 7.2 Examples of interactions of carrying and carried types -- 7.3 Equations of motion in Routh’s form -- 8 Synchronisation of anisochronous objects with a single degree of freedom -- 8.1 Eliminating coordinates of the carrying system -- 8.2 The principal resonance in the system with weak carrying interactions -- 8.3 Dynamic matrix and harmonic influence coefficients of the carrying system -- 8.4 Synchronisation of the force exciters of the simplest type -- 8.5 Extremum properties of stationary synchronous motions -- 8.6 Synchronisation in a piecewise continuous system -- 9 Synchronisation of inertial vibration exciters -- 9.1 Inertial vibration exciter generated by rotational forces -- 9.2 The case of a single vibration exciter mounted on a carrying system --  
653 |a Mechanics, Applied 
653 |a Materials Science, general 
653 |a Mathematical analysis 
653 |a Computational intelligence 
653 |a Statistical physics 
653 |a Materials science 
653 |a Theoretical and Applied Mechanics 
653 |a Complex Systems 
653 |a Classical Mechanics 
653 |a Computational Intelligence 
653 |a Analysis (Mathematics) 
653 |a Mechanics 
653 |a Dynamical systems 
653 |a Analysis 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b SBA  |a Springer Book Archives -2004 
490 0 |a Foundations of Engineering Mechanics 
856 |u https://doi.org/10.1007/978-3-540-45761-9?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 620.1 
520 |a This book presents a rational scheme of analysis for the periodic and quasi-periodic solution of a broad class of problems within technical and celestial mechanics. It develops steps for the determination of sufficiently general averaged equations of motion, which have a clear physical interpretation and are valid for a broad class of weak-interaction problems in mechanics. The criteria of stability regarding stationary solutions of these equations are derived explicitly and correspond to the extremum of a special "potential" function. Much consideration is given to applications in vibrational technology, electrical engineering and quantum mechanics, and a number of results are presented that are immediately useful in engineering practice. The book is intended for mechanical engineers, physicists, as well as applied mathematicians specializing in the field of ordinary differential equations