Verfügbarkeit: Foundations of mechanics | Technische Universität München

Foundations of mechanics:

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Bibliographische Detailangaben
Beteiligte Personen:	Abraham, Ralph 1936- (VerfasserIn), Marsden, Jerrold E. 1942-2010 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Providence, RI AMS Chelsea Publ. 2008
Ausgabe:	2. ed.
Schlagwörter:	Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik Mechanik Differentialgeometrie Himmelsmechanik Mathematik Theoretische Mechanik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016734611&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Originally publ.: Reading, Mass. : Benjamin/Cummings Pub., 1978. Includes bibliographical references and index
Umfang:	XXIV, 826 S. Ill., graph. Darst.
ISBN:	9780821844380

Internformat

MARC


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245	1	0	\|a Foundations of mechanics \|c Ralph Abraham ; Jerrold E. Marsden
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Datensatz im Suchindex

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adam_text	Contents Preface to the AMS Chelsea Edition ...................................xiii Preface to the Second Edition ..........................................xv Preface to the First Edition ............................................xvii Introduction ............................................................xix Preview ................................................................xx»· PARTI PRELIMINARIES 1 Chapter 1. Differential Theory .........................3 1.1 Topology ..............................3 Exercises ..............................17 1.2 Finite-Dimensional Banach Spaces ...............17 Exercises ..............................19 1.3 Local Differential Calculus ...................20 Exercises ..............................30 1.4 Manifolds and Mappings ....................31 Exercises ..............................36 1.5 Vector Bundles ..........................37 Exercises ..............................41 1.6 The Tangent Bundle .......................42 vil vlil CONTENTS Exercises ..............................50 1.7 Tensors..............................52 Exercises ..............................59 Chapter 2. Calculus on Manifolds .....................60 2.1 Vector Fields as Dynamical Systems ..............60 Exercises ..............................78 2.2 Vector Fields as Differential Operators .............78 Exercises ..............................98 2.3 Exterior Algebra .........................101 Exercises .............................109 2.4 Cartan s Calculus of Differential Forms ...........109 Exercises .............................121 2.5 Orientable Manifolds ......................122 Exercises .............................131 2.6 Integration on Manifolds ....................131 Exercises .............................143 2.7 Some Riemannian Geometry ..................144 Exercises .............................156 PART II ANAL YTICAL DYNAMICS 159 Chapters. Hamiltonian and Lagrangian Systems ............161 3.1 Symplectic Algebra .......................161 Exercises .............................174 3.2 Symplectic Geometry ......................174 Exercises .............................185 3.3 Hamiltonian Vector Fields and Poisson Brackets ......187 Exercises .............................199 3.4 Integral Invariants, Energy Surfaces, and Stability .....201 Exercises .............................208 3.5 Lagrangian Systems .......................208 Exercises .............................217 3.6 The Legendre Transformation .................218 Exercises .............................223 3.7 Mechanics on Riemannian Manifolds .............224 Exercises .............................244 3.8 Variational Principles in Mechanics ..............246 Exercises .............................252 Chapter 4. Hamiltonian Systems with Symmetry ............253 4.1 Lie Groups and Group Actions ................253 Exercises .............................271 CONTENTS lx 4.2 The Momentum Mapping ...................276 Exercises .............................295 4.3 Reduction of Phase Spaces with Symmetry ..........298 Exercises .............................309 4.4 Hamiltonian Systems on Lie Groups and the Rigid Body . .311 Exercises ............................. 338 4.5 The Topology of Simple Mechanical Systems ........338 Exercises .............................359 4.6 The Topology of the Rigid Body ................360 Exercises .............................368 Chapter 5. Hamllton-Jacobi Theory and Mathematical Physics .... 370 5.1 Time-Dependent Systems ....................370 Exercises .............................378 5.2 Canonical Transformations and Hamilton-Jacobi Theory . 379 Exercises .............................400 5.3 Lagrangian Submanifolds ...................402 Exercises .............................420 5.4 Quantization ...........................425 5.5 Introduction to Infinite-Dimensional Hamiltonian Systems .453 Exercises .............................486 5.6 Introduction to Nonlinear Oscillations ............489 PART III AN OUTLINE OF QUALITATIVE DYNAMICS 507 Chapter 6. Topologica! Dynamics .....................509 6.1 Limit and Minimal Sets .....................509 Exercises .............................513 6.2 Recurrence ............................513 Exercises .............................515 6.3 Stability .............................515 Exercises .............................519 Chapter 7. Differentiable Dynamics ....................520 7.1 Critical Elements ........................520 Exercises .............................525 7.2 Stable Manifolds ........................525 Exercises .............................531 7.3 Generic Properties ........................531 Exercises .............................534 7.4 Structural Stability .......................534 Exercises .............................536 ι CONTENTS 7.5 Absolute Stability and Axiom A ................536 Exercises .............................542 7.6 Bifurcations of Generic Arcs ..................543 Exercises .............................548 7.7 A Zoo of Stable Bifurcations ..................548 7.8 Experimental Dynamics ....................570 Chapter 8. Hamiltonian Dynamics .....................572 8.1 Critical Elements ........................572 8.2 Orbit Cylinders .........................576 Exercises .............................579 8.3 Stability of Orbits ........................579 Exercises .............................587 8.4 Generic Properties ........................587 8.5 Structural Stability .......................592 8.6 A Zoo of Stable Bifurcations ..................595 8.7 The General Pathology .....................606 8.8 Experimental Mechanics ....................610 PART IV CELESTIAL MECHANICS 617 ChapterD. The Two-Body Problem ....................619 9.1 Models for Two Bodies .....................619 Exercises .............................624 9.2 Elliptic Orbits and Kepler Elements ..............624 9.3 The Delaunay Variables ....................631 9.4 Lagrange Brackets of Kepler Elements ............635 9.5 Whittaker s Method .......................638 9.6 Poincaré Variables .......................647 Exercises .............................652 9.7 Summary of Models .......................652 Exercise .............................656 9.8 Topology of the Two-Body Problem .............656 Chapter 10. The Three-Body Problem ...................663 10.1 Models for Three Bodies ....................663 Exercises .............................673 10.2 Critical Points in the Restricted Three-Body Problem . . . .675 Exercises .............................687 10.3 Closed Orbits in the Restricted Three-Body Problem .... 688 Exercises .............................699 10.4 Topology of the Planar л -Body Problem ...........699 CONTENTS xl Appendix The General Theory of Dynamical Systems and Classical Mechanics by A. N. Kolmogorov ..........741 Bibliography ...................................759 Index .......................................791 Glossary of Symbols ...................................................807 Errata ..................................................................809
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spellingShingle	Abraham, Ralph 1936- Marsden, Jerrold E. 1942-2010 Foundations of mechanics Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik (DE-588)4013384-9 gnd Mechanik (DE-588)4038168-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Himmelsmechanik (DE-588)4127484-2 gnd Mathematik (DE-588)4037944-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd
subject_GND	(DE-588)4013384-9 (DE-588)4038168-7 (DE-588)4012248-7 (DE-588)4127484-2 (DE-588)4037944-9 (DE-588)4185100-6
title	Foundations of mechanics
title_auth	Foundations of mechanics
title_exact_search	Foundations of mechanics
title_full	Foundations of mechanics Ralph Abraham ; Jerrold E. Marsden
title_fullStr	Foundations of mechanics Ralph Abraham ; Jerrold E. Marsden
title_full_unstemmed	Foundations of mechanics Ralph Abraham ; Jerrold E. Marsden
title_short	Foundations of mechanics
title_sort	foundations of mechanics
topic	Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik (DE-588)4013384-9 gnd Mechanik (DE-588)4038168-7 gnd Differentialgeometrie (DE-588)4012248-7 gnd Himmelsmechanik (DE-588)4127484-2 gnd Mathematik (DE-588)4037944-9 gnd Theoretische Mechanik (DE-588)4185100-6 gnd
topic_facet	Géométrie différentielle Mécanique analytique Mécanique céleste Mechanics, Analytic Geometry, Differential Celestial mechanics Dynamik Mechanik Differentialgeometrie Himmelsmechanik Mathematik Theoretische Mechanik
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Bestandsangaben von Handapparate (nicht verfügbar)
Signatur:	0049 PHY 200f 2010 B 321(2) Lageplan
Exemplar 1	Dauerhaft ausgeliehen Ausgeliehen – Rückgabe bis: 31.12.9999