Screen LibraryTheory of oscillations /
This monograph deals with the controlled/non-controlled nonlinear systems of differential equations. A mathematical apparatus is developed to construct stationary conditions and to carry out studies on the behaviour of integral curves in the neighbourhood of such conditions.Considerable coverage is...
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| Main Authors: | |
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| Corporate Authors: | |
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 1999. |
| Literature type: | eBook |
| Language: |
English Russian |
| Series: |
Series on optimization ;
vol. 4 |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/1669#t=toc |
| Summary: |
This monograph deals with the controlled/non-controlled nonlinear systems of differential equations. A mathematical apparatus is developed to construct stationary conditions and to carry out studies on the behaviour of integral curves in the neighbourhood of such conditions.Considerable coverage is given to existence and methods of finding periodic orbits and almost-periodic solutions, as well as to the description of the class of ergodic recurrent motions. There is further treatment of the perturbation method and the theory of time-independent and periodic perturbations in particular.The theory developed here is applied to the construction and investigation of the neigbourhood of time-independent conditions for nonlinear systems of automatic control, and the control of charged particle beam in magnetic field. Some other specific problems are also solved such as after effect systems and orbit quantization. |
| Carrier Form: | 1 online resource (viii,399pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 393-395) and index. |
| ISBN: | 9789812817570 |
| Index Number: | QA865 |
| CLC: | O32 |
| Contents: | 1. Preliminary representations and analyses of motion family behavior. 1.1. Basic properties of functions defined by ordinary differential equations. 1.2. Properties of solutions to linear systems. 1.3. Behavior of integral curves of a nonlinear system of ODE's with unbounded increase in time. 1.4. Behavior of integral curves in the neighborhood of a singular point. 1.5. Lyapunov stability of nonperturbed motions -- 2. On behavior of trajectories in the neighborhood of a periodic orbit. 2.1. Autonomous dynamical systems. 2.2. Preliminary studies on properties of the neighborhood of a periodic orbit. 2.3. unity roots of characteristic equation. 2.4. the case of several complex roots with unity moduli. 2.5. Perturbation theory of periodic orbits -- 3. Natural and forced oscillations in systems with many degrees of freedom. 3.1. Basic properties of periodic dynamical systems. 3.2. Small parameter method. 3.3. Natural oscillations of autonomous systems in a neighborhood of an equilibrium. 3.4. Forced periodic and almost periodic oscillations. 3.5. Influence of external perturbations on stationary modes -- 4. Methods for investigation and construction of stationary modes. 4.1. Elements of recurrent function theory. 4.2. Forced multifrequency oscillations. 4.3. Motions of nonlinear systems determined by boundary conditions. 4.4. Application of method of successive approximations for finding stationary modes -- 4.5. Quantitative stability criteria for stationary modes in automatic control systems -- 5. Oscillations in nonlinear and controlled systems. 5.1. Construction and investigation of stationary self-oscillations in automatic control systems. 5.2. Self-oscillations in hysteresis systems. 5.3. Controlled motion of charged particles in magnetic field. 5.4. Phase plane. 5.5. Oscillations in autonomous system. 5.6. Analytical test for qualitative behavior of integral curves on a plane in the neighborhood of periodic motion. |