LEADER 03985nam 2200505 450 001 9910793252203321 005 20230817191115.0 010 $a3-11-054297-8 010 $a3-11-054444-X 024 7 $a10.1515/9783110544442 035 $a(CKB)4100000007205106 035 $a(MiAaPQ)EBC5159082 035 $a(DE-B1597)480859 035 $a(OCoLC)1078919900 035 $a(DE-B1597)9783110544442 035 $a(Au-PeEL)EBL5159082 035 $a(OCoLC)1085186069 035 $a(EXLCZ)994100000007205106 100 $a20190309d2019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRigid body dynamics /$fAlexey V. Borisov, Ivan S. Mamaev 210 1$aBerlin ;$aBoston :$cDe Gruyter :$cHigher Education Press,$d2019. 215 $a1 online resource (530 pages) 225 1 $aDe Gruyter Studies in Mathematical Physics 311 $a3-11-054279-X 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tThe Creators of Rigid Body Dynamics -- $t1. Rigid Body Equations of Motion and Their Integration -- $t2. The Euler - Poisson Equations and Their Generalizations -- $t3. The Kirchhoff Equations and Related Problems of Rigid Body Dynamics -- $t4. Linear Integrals and Reduction -- $t5. Generalizations of Integrability Cases. Explicit Integration -- $t6. Periodic Solutions, Nonintegrability, and Transition to Chaos -- $tA. Derivation of the Kirchhoff, Poincaré - Zhukovskii, and Four-Dimensional Top Equations -- $tB. The Lie Algebra e(4) and Its Orbits -- $tC. Quaternion Equations and L-A Pair for the Generalized Goryachev - Chaplygin Top -- $tD. The Hess Case and Quantization of the Rotation Number -- $tE. Ferromagnetic Dynamics in a Magnetic Field -- $tF. The Landau - Lifshitz Equation, Discrete Systems, and the Neumann Problem -- $tG. Dynamics of Tops and Material Points on Spheres and Ellipsoids -- $tH. On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation -- $tI. The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids -- $tBibliography -- $tIndex of Names -- $tIndex 330 $aThis book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler - Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré - Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev - Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau - Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids 410 0$aDe Gruyter studies in mathematical physics. 606 $aDynamics, Rigid 615 0$aDynamics, Rigid. 676 $a531.3 686 $aUF 1950$qBVB$2rvk 700 $aBorisov$b A. V$g(Aleksei? Vladimirovich),$01562113 702 $aMamaev$b Ivan S. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793252203321 996 $aRigid body dynamics$93829442 997 $aUNINA