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Lagrangian & Hamiltonian dynamics:

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Beteilige Person:	Mann, Peter (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Oxford Oxford University Press 2018
Ausgabe:	First edition
Schlagwörter:	Lagrange-Formalismus Hamilton-Formalismus Theoretische Mechanik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030306943&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030306943&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xiv, 538 Seiten Illustrationen, Diagramme (teilweise farbig)
ISBN:	9780198822370 9780198822387

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Datensatz im Suchindex

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adam_text	Contents A Preface xiii PART I NEWTONIAN MECHANICS 1 Newton’s Three Laws 3 1.1 Phase Space 7 1.2 Systems of Particles 8 1.3 The N-body Problem 11 Chapter summary 13 2 Energy and Work 15 Chapter summary 22 3 Introductory Rotational Dynamics 24 Chapter summary 33 4 The Harmonic Oscillator 34 Chapter summary 38 5 Wave Mechanics fe Elements of Mathematical Physics 44 PART II LAGRANGIAN MECHANICS 6 Coordinates 8z Constraints 55 Chapter summary 59 7 The Stationary Action Principle 61 7.1 The Inverse Problem 70 7.2 Higher-Order Theories the Ostrogradsky Equation 72 7.3 The Second Variation 73 7.4 Functions Functionals 74 7.5 Boundary Conditions 76 7.6 Variations 78 7.7 Weierstrass-Erdmann Conditions for Broken Extremals 79 7.8 Hamilton-Suslov Principle 79 Chapter summary 80 8 Constrained Lagrangian Mechanics 89 8.1 Holonomic Constraints 89 viii Contents 8.2 Non-Holonomic Constraints 93 Chapter summary 96 9 Point Transformations in Lagrangian Mechanics 100 Chapter summary 103 10 The Jacobi Energy Function 107 Chapter summary 112 11 Symmetries Lagrangian-Hamilton-Jacobi Theory 115 11.1 Noether’s Theorem 115 11.2 Gauge Theory 120 11.3 Isotropic Symmetries 122 11.4 Caratheodory-Hamilton-Jacobi theory 123 Chapter summary 124 12 Near-Equilibrium Oscillations 130 12.1 Normal Modes 137 Chapter summary 140 13 Virtual Work d’Alembert’s Principle 147 13.1 Gauss’s Least Constraint Jourdain’s Principle 153 13.2 The Gibbs-Appell Equations 156 Chapter summary 158 PART III CANONICAL MECHANICS 14 The Hamiltonian Phase Space 167 Chapter summary 172 15 Hamilton’s Principle in Phase Space 174 Chapter summary 178 16 Hamilton’s Equations Routhian Reduction 179 16.1 Phase Space Conservation Laws 181 16.2 Routhian Mechanics 183 17 Poisson Brackets ; Angular Momentum 190 17.1 Poisson Brackets Angular Momenta 195 17.2 Poisson Brackets Symmetries 197 Chapter summary 200 18 Canonical ; Gauge Transformations 202 18.1 Canonical Transformations I 202 18.2 Canonical Transformations II 206 Contents ix 18.3 Infinitesimal Canonical Transformations 211 Chapter summary 214 19 Hamilton-Jacobi Theory 217 19.1 Hamilton-Jacobi Theory I 217 19.2 Hamilton-Jacobi Theory II 224 Chapter summary 229 20 Liouville’s Theorem ; Classical Statistical Mechanics 237 20.1 Liouville’s Theorem k the Classical Propagator 237 20.2 Koopman-von Neumann Theory 244 20.3 Classical Statistical Mechanics 246 20.4 Symplectic Integrators 255 Chapter summary 259 21 Constrained Hamiltonian Dynamics 267 Chapter summary 274 22 Autonomous Geometrical Mechanics 277 22.1 A Coordinate-Free Picture 284 22.2 Poisson Manifolds k Symplectic Reduction 291 22.3 Geometrical Lagrangian Mechanics 296 22.4 Elements of Constrained Geometry 300 Chapter summary 303 23 The Structure of Phase Space 309 23.1 Time-Dependent Geometrical Mechanics 313 23.2 Picturing Phase Space 319 Chapter summary 322 24 Near-Integrable Systems 325 24.1 Canonical Perturbation Theory 325 24.2 KAM Theory k Elements of Chaos 333 PART IV CLASSICAL FIELD THEORY 25 Lagrangian Field Theory 345 Chapter summary 350 26 Hamiltonian Field Theory 353 27 Classical Electromagnetism 357 Chapter summary 365 x Contents 28 Noether’s Theorem for Fields Chapter summary 29 Classical Path-Integrals 29.1 Configuration Space Integrals 29.2 Phase Space Integrals PART V PRELIMINARY MATHEMATICS 30 The (Not So?) Basics 31 Matrices 32 Partial Differentiation 33 Legendre Transforms 34 Vector Calculus 35 Differential Equations 36 Calculus of Variations PART VI ADVANCED MATHEMATICS 37 Linear Algebra 38 Differential Geometry PART VII EXAM-STYLE QUESTIONS Appendix A Noether’s Theorem Explored Appendix B The Action Principle Explored B.l Geodesics Appendix C Useful Relations Appendix D Poisson ; Nambu Brackets Explored D.l Symplectic Notation Nambu Brackets Appendix E Canonical Transformations Explored Appendix F Action-Angle Variables Explored Appendix G Statistical Mechanics Explored G.l The Boltzmann Factor G.2 Fluctuations 369 376 385 385 386 397 400 406 419 422 437 443 453 460 487 491 491 494 496 497 502 506 511 511 512 Contents xi Appendix H Biographies 514 H.l Sir Isaac Newton 514 H.2 Leonhard Euler 515 H.3 Jean d’Alembert 516 H.4 Joseph-Louis Lagrange 517 H.5 Carl Gustav Jacobi 519 H.6 Sir William Hamilton 520 H.7 Siméon Denis Poisson 522 H.8 Amalie Emmy Noether 522 H.9 Ludwig Eduard Boltzmann 524 H.10 Edward Routh 525 H.ll Hendrika van Leeuwen 526 Bibliography Index 527 533 An introductory textbook exploring the subject of Lagrangian and Hamiltonian dynamics with a relaxed and self-contained setting, for those unacquainted with mathematics or university level physics. Lagrangian and Hamiltonian dynamics is the continuation of Newton’s classical physics into new formalisms, each highlighting novel aspects of mechanics and gradually building in complexity to form the basis for almost all of theoretical physics. Lagrangian and Hamiltonian dynamics also acts as a gateway to more abstract concepts rooted in differential geometry and field theories and can be used to introduce these subject areas to newcomers. Journeying in a self-contained manner from the very basics, through the fundamentals and onwards to the cutting edge of the subject, along the way the reader is supported by all the necessary background mathematics, fully worked examples and thoughtful and vibrant illustrations, as well as an informal narrative and numerous fresh, modern and interdisciplinary applications. The book contains some unusual topics for a classical mechanics textbook: notable examples include the classical wavefunction’, Koopman-von Neumann theory, classical density functional theories, the ‘vakonomic’ variational principle for non-holonomic constraints, the Gibbs-Appell equations, classical path integrals. Nambu brackets and the full framing of mechanics in the language of differential geometry. Alongside these is a very detailed and explicit account of Lagrangian and Hamiltonian dynamics, an account that ventures above and beyond that presented in most undergraduate courses.
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spellingShingle	Mann, Peter Lagrangian & Hamiltonian dynamics Lagrange-Formalismus (DE-588)4316154-6 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Theoretische Mechanik (DE-588)4185100-6 gnd
subject_GND	(DE-588)4316154-6 (DE-588)4376155-0 (DE-588)4185100-6
title	Lagrangian & Hamiltonian dynamics
title_alt	Langrangian and Hamiltonian dynamics
title_auth	Lagrangian & Hamiltonian dynamics
title_exact_search	Lagrangian & Hamiltonian dynamics
title_full	Lagrangian & Hamiltonian dynamics Peter Mann, University of St Andrews
title_fullStr	Lagrangian & Hamiltonian dynamics Peter Mann, University of St Andrews
title_full_unstemmed	Lagrangian & Hamiltonian dynamics Peter Mann, University of St Andrews
title_short	Lagrangian & Hamiltonian dynamics
title_sort	lagrangian hamiltonian dynamics
topic	Lagrange-Formalismus (DE-588)4316154-6 gnd Hamilton-Formalismus (DE-588)4376155-0 gnd Theoretische Mechanik (DE-588)4185100-6 gnd
topic_facet	Lagrange-Formalismus Hamilton-Formalismus Theoretische Mechanik
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