| Description |
1 online resource (xii, 197 pages) : illustrations (some color) |
| Series |
Understanding complex systems, 1860-0832 |
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Springer complexity |
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Understanding complex systems, 1860-0832
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Springer complexity.
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| Contents |
Intro -- Preface -- References -- Contents -- About the Authors -- 1 Autonomous and Non-autonomous Systems with One Degree of Freedom -- 1.1 Dynamics of Autonomous Rotator and Related Physical Systems -- 1.2 Synchronization and Chaotic Rotations of Non-autonomous Rotator -- References -- 2 Autonomous and Non-autonomous Systems with One and a Half Degrees of Freedom -- 2.1 Dynamics of Rotator with Aperiodic Load -- 2.2 Synchronization and Dynamical Chaos in a System of Non-autonomous Rotator with Aperiodic Load -- References -- 3 Autonomous Systems with Two Degrees of Freedom |
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3.1 Dynamics of Rotator with Oscillatory Load -- 3.2 Chaotic Dynamics of a Simple Vibrational Mechanism -- 3.3 Dynamics of Coupled Rotators -- References -- 4 Vibration of Shafts -- 4.1 Nonlinear Resonance of Bending Vibrations of a Flexible Rotor in a System with an Energy Source of Limited Power -- 4.2 Damping Lateral Vibrations in Rotary Machinery Using Motor Speed Modulation -- 4.3 Chaotic Torsional Vibrations of the Shaft in a System with Limited Power Source -- References -- 5 Synchronization in Homogeneous Lattices |
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5.1 Synchronization in Lattices of Dynamical Systems. General Information -- 5.2 Synchronization of Rotations in a Chain and in a Ring of Diffusive-Coupled Autonomous and Non-autonomous Rotators -- 5.3 Regular and Chaotic Synchronization in a Homogeneous Chain of Dynamical Systems of "Rotator-Oscillator" Type -- References -- 6 Physics, Existence, Fusion, and Stability of Cluster Structures -- 6.1 Physics of Cluster Structures -- 6.2 Fusion and General Properties of Circuits of Cluster Structures -- 6.3 C-Oscillators of a Chain and the Fullness of Types of Their Cluster Structures |
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6.4 C-Oscillators of a Ring and Fusion of Cluster Structures -- 6.5 Stability of Cluster Structures -- References -- Appendix A Algorithms of Transformation of Systems of Coupled Rotators to the Standard Form -- A.1 Systems of Coupled Rotators Without Additional Loads -- A.2 Systems of Coupled Rotators with Aperiodic Loads -- A.3 Systems of Coupled Rotators with Oscillatory Loads -- Appendix B Calculation of Eigenvalues of Matrices |
| Summary |
This book develops analytical methods for studying the dynamical chaos, synchronization, and dynamics of structures in various models of coupled rotators. Rotators and their systems are defined in a cylindrical phase space, and, unlike oscillators, which are defined in Rn, they have a wider "range" of motion: There are vibrational and rotational types for cyclic variables, as well as their combinations (rotational-vibrational) if the number of cyclic variables is more than one. The specificity of rotator phase space poses serious challenges in terms of selecting methods for studying the dynamics of related systems. The book chiefly focuses on developing a modified form of the method of averaging, which can be used to study the dynamics of rotators. In general, the book uses the "language" of the qualitative theory of differential equations, point mappings, and the theory of bifurcations, which helps authors to obtain new results on dynamical chaos in systems with few degrees of freedom. In addition, a special section is devoted to the study and classification of dynamic structures that can occur in systems with a large number of interconnected objects, i.e. in lattices of rotators and/or oscillators. Given its scope and format, the book can be used both in lectures and courses on nonlinear dynamics, and in specialized courses on the development and operation of relevant systems that can be represented by a large number of various practical systems: interconnected grids of various mechanical systems, various types of networks including not only mechanical but also biological systems, etc |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed January 22, 2020) |
| Subject |
Rotational motion.
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Chaotic behavior in systems.
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Rotation
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rotation.
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Chaotic behavior in systems
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Rotational motion
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| Form |
Electronic book
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| Author |
Verichev, Stanislav, author
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Erofeev, Vladimir, author.
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| ISBN |
9783030361037 |
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3030361039 |
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