Verfügbarkeit: Introduction to mechanics and symmetry

Introduction to mechanics and symmetry: a basic exposition of classical mechanical systems

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Bibliographische Detailangaben
Beteiligte Personen:	Marsden, Jerrold E. 1942-2010 (VerfasserIn), Ratiu, Tudor S. (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Springer 1999
Ausgabe:	2. ed.
Schriftenreihe:	Texts in applied mathematics 17
Schlagwörter:	Theoretische Mechanik - Symmetrie Mechanics, Analytic Symmetry (Physics) Symmetrie Mechanik Theoretische Mechanik Hamiltonsches System
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008535566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Umfang:	XVIII, 582 S. graph. Darst.
ISBN:	038798643X 9781441931436

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface ix About the Authors xiii 1 Introduction and Overview 1 1.1 Lagrangian and Hamiltonian Formalisms 1 1.2 The Rigid Body 6 1.3 Lie Poisson Brackets, Poisson Manifolds, Momentum Maps 9 1.4 The Heavy Top 16 1.5 Incompressible Fluids 18 1.6 The Maxwell Vlasov System 22 1.7 Nonlinear Stability 29 1.8 Bifurcation 43 1.9 The Poincare Melnikov Method 47 1.10 Resonances, Geometric Phases, and Control 50 2 Hamiltonian Systems on Linear Symplectic Spaces 61 2.1 Introduction 61 2.2 Symplectic Forms on Vector Spaces 66 2.3 Canonical Transformations, or Symplectic Maps 69 2.4 The General Hamilton Equations 74 2.5 When Are Equations Hamiltonian? 77 2.6 Hamiltonian Flows 80 2.7 Poisson Brackets 82 xvi Contents 2.8 A Particle in a Rotating Hoop 87 2.9 The Poincare Melnikov Method 94 3 An Introduction to Infinite Dimensional Systems 105 3.1 Lagrange s and Hamilton s Equations for Field Theory . . 105 3.2 Examples: Hamilton s Equations 107 3.3 Examples: Poisson Brackets and Conserved Quantities . . 115 4 Manifolds, Vector Fields, and Differential Forms 121 4.1 Manifolds 121 4.2 Differential Forms 129 4.3 The Lie Derivative 137 4.4 Stokes Theorem 141 5 Hamiltonian Systems on Symplectic Manifolds 147 5.1 Symplectic Manifolds 147 5.2 Symplectic Transformations 150 5.3 Complex Structures and Kahler Manifolds 152 5.4 Hamiltonian Systems 157 5.5 Poisson Brackets on Symplectic Manifolds 160 6 Cotangent Bundles 165 6.1 The Linear Case 165 6.2 The Nonlinear Case 167 6.3 Cotangent Lifts 170 6.4 Lifts of Actions 173 6.5 Generating Functions 174 6.6 Fiber Translations and Magnetic Terms 176 6.7 A Particle in a Magnetic Field 178 7 Lagrangian Mechanics 181 7.1 Hamilton s Principle of Critical Action 181 7.2 The Legendre Transform 183 7.3 Euler Lagrange Equations 185 7.4 Hyperregular Lagrangians and Hamiltonians 188 7.5 Geodesies 195 7.6 The Kaluza Klein Approach to Charged Particles 200 7.7 Motion in a Potential Field 202 7.8 The Lagrange d Alembert Principle 205 7.9 The Hamilton Jacobi Equation 210 8 Variational Principles, Constraints, Rotating Systems 219 8.1 A Return to Variational Principles 219 8.2 The Geometry of Variational Principles 226 8.3 Constrained Systems 234 Contents xvii 8.4 Constrained Motion in a Potential Field 238 8.5 Dirac Constraints 242 8.6 Centrifugal and Coriolis Forces 248 8.7 The Geometric Phase for a Particle in a Hoop 253 8.8 Moving Systems 257 8.9 Routh Reduction 260 9 An Introduction to Lie Groups 265 9.1 Basic Definitions and Properties 267 9.2 Some Classical Lie Groups 283 9.3 Actions of Lie Groups 309 10 Poisson Manifolds 327 10.1 The Definition of Poisson Manifolds 327 10.2 Hamiltonian Vector Fields and Casimir Functions 333 10.3 Properties of Hamiltonian Flows 338 10.4 The Poisson Tensor 340 10.5 Quotients of Poisson Manifolds 349 10.6 The Schouten Bracket 353 10.7 Generalities on Lie Poisson Structures 360 11 Momentum Maps 365 11.1 Canonical Actions and Their Infinitesimal Generators . . 365 11.2 Momentum Maps 367 11.3 An Algebraic Definition of the Momentum Map 370 11.4 Conservation of Momentum Maps 372 11.5 Equivariance of Momentum Maps 378 12 Computation and Properties of Momentum Maps 383 12.1 Momentum Maps on Cotangent Bundles 383 12.2 Examples of Momentum Maps 389 12.3 Equivariance and Infinitesimal Equivariance 396 12.4 Equivariant Momentum Maps Are Poisson 403 12.5 Poisson Automorphisms 412 12.6 Momentum Maps and Casimir Functions 413 13 Lie—Poisson and Euler—Poincare Reduction 417 13.1 The Lie Poisson Reduction Theorem 417 13.2 Proof of the Lie Poisson Reduction Theorem for GL^n) . 420 13.3 Lie Poisson Reduction Using Momentum Functions .... 421 13.4 Reduction and Reconstruction of Dynamics 423 13.5 The Euler Poincare Equations 432 13.6 The Lagrange Poincare Equations 442 xviii Contents 14 Coadjoint Orbits 445 14.1 Examples of Coadjoint Orbits 446 14.2 Tangent Vectors to Coadjoint Orbits 453 14.3 The Symplectic Structure on Coadjoint Orbits 455 14.4 The Orbit Bracket via Restriction of the Lie Poisson Bracket461 14.5 The Special Linear Group of the Plane 467 14.6 The Euclidean Group of the Plane 469 14.7 The Euclidean Group of Three Space 474 15 The Free Rigid Body 483 15.1 Material, Spatial, and Body Coordinates 483 15.2 The Lagrangian of the Free Rigid Body 485 15.3 The Lagrangian and Hamiltonian in Body Representation 487 15.4 Kinematics on Lie Groups 491 15.5 Poinsot s Theorem 492 15.6 Euler Angles 495 15.7 The Hamiltonian of the Free Rigid Body 497 15.8 The Analytical Solution of the Free Rigid Body Problem . 500 15.9 Rigid Body Stability 505 15.10 Heavy Top Stability 509 15.11 The Rigid Body and the Pendulum 514 References 521 Index 555
any_adam_object	1
author	Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S.
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author_facet	Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S.
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dewey-ones	531 - Classical mechanics
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spellingShingle	Marsden, Jerrold E. 1942-2010 Ratiu, Tudor S. Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Texts in applied mathematics Theoretische Mechanik - Symmetrie Mechanics, Analytic Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd
subject_GND	(DE-588)4058724-1 (DE-588)4038168-7 (DE-588)4185100-6 (DE-588)4139943-2
title	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_auth	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_exact_search	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_full	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu
title_fullStr	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu
title_full_unstemmed	Introduction to mechanics and symmetry a basic exposition of classical mechanical systems Jerrold E. Marsden ; Tudor S. Ratiu
title_short	Introduction to mechanics and symmetry
title_sort	introduction to mechanics and symmetry a basic exposition of classical mechanical systems
title_sub	a basic exposition of classical mechanical systems
topic	Theoretische Mechanik - Symmetrie Mechanics, Analytic Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Hamiltonsches System (DE-588)4139943-2 gnd
topic_facet	Theoretische Mechanik - Symmetrie Mechanics, Analytic Symmetry (Physics) Symmetrie Mechanik Theoretische Mechanik Hamiltonsches System
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008535566&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV002476038
work_keys_str_mv	AT marsdenjerrolde introductiontomechanicsandsymmetryabasicexpositionofclassicalmechanicalsystems AT ratiutudors introductiontomechanicsandsymmetryabasicexpositionofclassicalmechanicalsystems

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