Beschreibung
Inhaltsverzeichnis
Locally integrable dynamical systems.- Conservative dynamical systems.- Dynamical systems in a plane.- Conservative systems with many degrees of freedom.- Resonant solutions for systems integrable in generating approximation.- Canonical averaging of the equations of quantum mechanics.- The problem of weak interaction of dynamical objects.- Synchronisation of anisochronous objects with a single degree of freedom.- Synchronisation of inertial vibration exciters.- Synchronisation of dynamical objects of the general type.- Periodic solutions in problems of excitation of mechanical oscillations.
Autorenporträt
Inhaltsangabe1 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.- 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.- 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.- 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.- 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
