Rigid Body Dynamics / / Alexey Borisov, Ivan S. Mamaev.
This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathe...
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Superior document: | Title is part of eBook package: De Gruyter DG Plus DeG Package 2019 Part 1 |
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2018] ©2019 |
Year of Publication: | 2018 |
Language: | English |
Series: | De Gruyter Studies in Mathematical Physics ,
52 |
Online Access: | |
Physical Description: | 1 online resource (VII, 526 p.) |
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Other title: | Frontmatter -- Contents -- Introduction -- The Creators of Rigid Body Dynamics -- 1. Rigid Body Equations of Motion and Their Integration -- 2. The Euler – Poisson Equations and Their Generalizations -- 3. The Kirchhoff Equations and Related Problems of Rigid Body Dynamics -- 4. Linear Integrals and Reduction -- 5. Generalizations of Integrability Cases. Explicit Integration -- 6. Periodic Solutions, Nonintegrability, and Transition to Chaos -- A. Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations -- B. The Lie Algebra e(4) and Its Orbits -- C. Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top -- D. The Hess Case and Quantization of the Rotation Number -- E. Ferromagnetic Dynamics in a Magnetic Field -- F. The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem -- G. Dynamics of Tops and Material Points on Spheres and Ellipsoids -- H. On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation -- I. The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids -- Bibliography -- Index of Names -- Index |
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Summary: | This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler – Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9783110544442 9783110762464 9783110719567 9783110645309 9783110616859 9783110604252 9783110603255 9783110604221 9783110603224 |
ISSN: | 2194-3532 ; |
DOI: | 10.1515/9783110544442 |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Alexey Borisov, Ivan S. Mamaev. |