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Mathematical methods of cla...
Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians
Monografía
monografia Rebiun35819871 https://catalogo.rebiun.org/rebiun/record/Rebiun35819871 m o d cr bn||||||abp cr bn||||||ada 101117s1978 nyua ob 001 0 eng d 624481021 913437352 1001480334 1012474744 1016369874 1196194143 1302160032 1408987075 9781475716931 electronic bk.) 1475716931 electronic bk.) 9781475716955 print) 1475716958 print) 0387903143 New York) 9780387903149 New York) 3540903143 9783540903147 10.1007/978-1-4757-1693-1 doi AU@ 000057642530 NLGGC 401222403 NZ1 15754817 OCLCE eng pn OCLCE OCLCQ OCLCO OCLCQ GW5XE OCLCF COO OCLCQ UPM UAB OCLCQ OCLCO U3W AU@ OCLCQ OCLCO UKAHL OCLCQ OCLCO INARC OCLCQ OCLCO OCLCL eng rus dlr PB bicssc MAT000000 bisacsh Arnold, V. I. Vladimir Igorevich) 1937-2010.) https://id.oclc.org/worldcat/entity/E39PBJht4fhJ6BVBBMjxPtcMfq Matematicheskie metody klassicheskoi mekhaniki. English Mathematical methods of classical mechanics V.I. Arnold ; translated by K. Vogtmann and A. Weinstein New York Springer-Verlag 1978 New York New York Springer-Verlag 1 online resource (x, 462 pages) illustrations 1 online resource (x, 462 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF Graduate texts in mathematics 60 Includes bibliographical references and index I Newtonian Mechanics -- 1 Experimental facts -- 2 Investigation of the equations of motion -- II Lagrangian Mechanics -- 3 Variational principles -- 4 Lagrangian mechanics on manifolds -- 5 Oscillations -- 6 Rigid Bodies -- III Hamiltonian Mechanics -- 7 Differential forms -- 8 Symplectic manifolds -- 9 Canonical formalism -- 10 Introduction to perturbation theory -- Appendix 1 Riemannian curvature -- Appendix 2 Geodesies of left-invariant metrics on Lie groups and the hydrodynamics of an ideal fluid -- Appendix 3 Symplectic structure on algebraic manifolds -- Appendix 4 Contact structures -- Appendix 5 Dynamical systems with symmetries -- Appendix 6 Normal forms of quadratic hamiltonians -- Appendix 7 Normal forms of hamiltonian systems near stationary points and closed trajectories -- Appendix 8 Perturbation theory of conditionally periodic motions and Kolmogorov's theorem -- Appendix 9 Poincaré's geometric theorem, its generalizations and applications -- Appendix 10 Multiplicities of characteristic frequencies, and ellipsoids depending on parameters -- Appendix 11 Short wave asymptotics -- Appendix 12 Lagrangian singularities -- Appendix 13 The Korteweg-de Vries equation Use copy. Restrictions unspecified star. MiAaHDL Many different mathematical methods and concepts are used in classical mechanics: differential equations and phase ftows, smooth mappings and manifolds, Lie groups and Lie algebras, symplectic geometry and ergodic theory. Many modern mathematical theories arose from problems in mechanics and only later acquired that axiomatic-abstract form which makes them so hard to study. In this book we construct the mathematical apparatus of classical mechanics from the very beginning; thus, the reader is not assumed to have any previous knowledge beyond standard courses in analysis (differential and integral calculus, differential equations), geometry (vector spaces, vectors) and linear algebra (linear operators, quadratic forms). With the help of this apparatus, we examine all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the hamiltonian formalism. The author has tried to show the geometric, qualitative aspect of phenomena. In this respect the book is closer to courses in theoretical mechanics for theoretical physicists than to traditional courses in theoretical mechanics as taught by mathematicians Electronic reproduction. [Place of publication not identified] HathiTrust Digital Library 2010. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL Text in English, translated from the original Russian digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL Mechanics, Analytic Mécanique analytique Mechanics, Analytic. Mathematische Methode. Mechanik. Klassieke mechanica. Wiskundige methoden. Mechanics, Analytic. Mechanics, Analytic Print version Arnold, V.I. (Vladimir Igorevich), 1937-2010. Matematicheskie metody klassicheskoi mekhaniki. English. Mathematical methods of classical mechanics. New York : Springer-Verlag, 1978 (DLC) 78015927 (OCoLC)4037141 Graduate texts in mathematics 60