03985nam 2200505 450 991079325220332120230817191115.03-11-054297-83-11-054444-X10.1515/9783110544442(CKB)4100000007205106(MiAaPQ)EBC5159082(DE-B1597)480859(OCoLC)1078919900(DE-B1597)9783110544442(Au-PeEL)EBL5159082(OCoLC)1085186069(EXLCZ)99410000000720510620190309d2019 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierRigid body dynamics /Alexey V. Borisov, Ivan S. MamaevBerlin ;Boston :De Gruyter :Higher Education Press,2019.1 online resource (530 pages)De Gruyter Studies in Mathematical Physics3-11-054279-X 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 -- IndexThis 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 De Gruyter studies in mathematical physics.Dynamics, RigidDynamics, Rigid.531.3UF 1950BVBrvkBorisov A. V(Alekseĭ Vladimirovich),1562113Mamaev Ivan S.MiAaPQMiAaPQMiAaPQBOOK9910793252203321Rigid body dynamics3829442UNINA