LEADER 04145nam 22006975 450 001 9910792479103321 005 20210107015344.0 010 $a0-387-21792-4 024 7 $a10.1007/978-0-387-21792-5 035 $a(CKB)2660000000022237 035 $a(SSID)ssj0001297235 035 $a(PQKBManifestationID)11768583 035 $a(PQKBTitleCode)TC0001297235 035 $a(PQKBWorkID)11362230 035 $a(PQKB)10104624 035 $a(DE-He213)978-0-387-21792-5 035 $a(MiAaPQ)EBC3073308 035 $a(PPN)237978644 035 $a(EXLCZ)992660000000022237 100 $a20130321d1999 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Mechanics and Symmetry$b[electronic resource] $eA Basic Exposition of Classical Mechanical Systems /$fby Jerrold E. Marsden, Tudor S. Ratiu 205 $aSecond Edition. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1999. 215 $a1 online resource (XVIII, 586 p.) 225 1 $aTexts in Applied Mathematics,$x0939-2475 ;$v17 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4419-3143-0 327 $a1 Introduction and Overview -- 2 Hamiltonian Systems on Linear Symplectic Spaces -- 3 An Introduction to Infinite-Dimensional Systems -- 4 Manifolds, Vector Fields, and Differential Forms -- 5 Hamiltonian Systems on Symplectic Manifolds -- 6 Cotangent Bundles -- 7 Lagrangian Mechanics -- 8 Variational Principles, Constraints, & Rotating Systems -- 9 An Introduction to Lie Groups -- 10 Poisson Manifolds -- 11 Momentum Maps -- 12 Computation and Properties of Momentum Maps -- 13 Lie?Poisson and Euler?Poincaré Reduction -- 14 Coadjoint Orbits -- 15 The Free Rigid Body -- References. 330 $aSymmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available on-line. 410 0$aTexts in Applied Mathematics,$x0939-2475 ;$v17 606 $aPhysics 606 $aTopological groups 606 $aLie groups 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aPhysics 606 $aTheoretical, Mathematical and Computational Physics 606 $aTopological Groups, Lie Groups 606 $aManifolds and Cell Complexes (incl. Diff.Topology) 615 0$aPhysics. 615 0$aTopological groups. 615 0$aLie groups. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 14$aPhysics. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aTopological Groups, Lie Groups. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 676 $a530.1 700 $aMarsden$b Jerrold E$07790 702 $aRatiu$b Tudor S 801 0$bPQKB 906 $aBOOK 912 $a9910792479103321 996 $aIntroduction to mechanics and symmetry$9188773 997 $aUNINA