Verfügbarkeit: Mathematical methods of classical mechanics

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Bibliographische Detailangaben
Beteilige Person:	Arnolʹd, V. I. 1937-2010 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York [u.a.] Springer 1989
Ausgabe:	2. ed.
Schriftenreihe:	Graduate texts in mathematics 60
Schlagwörter:	Mekanik, Analitik Mécanique analytique Mechanics, Analytic Mechanik Theoretische Mechanik Mathematik Mathematische Methode Mathematische Physik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001239110&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Umfang:	IX, 508 S. Ill., zahlr. graph. Darst.
ISBN:	3540968903 0387968903

Internformat

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Datensatz im Suchindex

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adam_text	V. I. ARNOLD MATHEMATICAL METHODS OF CLASSICAL MECHANICS SECOND EDITION TRANSLATED BY K. VOGTMANN AND A. WEINSTEIN WITH 269 ILLUSTRATIONS SPRINGER CONTENTS PREFACE V PREFACE TO THE SECOND EDITION VII PART I NEWTONIAN MECHANICS L CHAPTER 1 EXPERIMENTAL FACTS 3 1. THE PRINCIPLES OF RELATIVITY AND DETERMINACY 3 2. THE GALILEAN GROUP AND NEWTON S EQUATIONS 4 3. EXAMPLES OF MECHANICAL SYSTEMS 11 CHAPTER 2 INVESTIGATION OF THE EQUATIONS OF MOTION 15 4. SYSTEMS WITH ONE DEGREE OF FREEDOM 15 5. SYSTEMS WITH TWO DEGREES OF FREEDOM 22 6. CONSERVATIVE FORCE FIELDS 28 7. ANGULAR MOMENTUM 30 8. INVESTIGATION OF MOTION IN A CENTRAL FIELD 33 9. THE MOTION OF A POINT IN THREE- SPACE 42 10. MOTIONS OF A SYSTEM OF N POINTS 44 11. THE METHOD OF SIMILARITY 50 PART II LAGRANGIAN MECHANICS 53 CHAPTER 3 VARIATIONAL PRINCIPLES 55 12. CALCULUS OF VARIATIONS 55 13. LAGRANGE S EQUATIONS 59 CONTENTS 14. LEGENDRE TRANSFORMATIONS 61 15. HAMILTON S EQUATIONS 65 16. LIOUVILLE S THEOREM 68 CHAPTER 4 LAGRANGIAN MECHANICS ON MANIFOLDS 75 17. HOLONOMIC CONSTRAINTS 75 18. DIFFERENTIABLE MANIFOLDS 77 19. LAGRANGIAN DYNAMICAL SYSTEMS 83 20. E. NOETHER S THEOREM 88 21. D ALEMBERT S PRINCIPLE 91 CHAPTER 5 OSCILLATIONS 98 22. LINEARIZATION 98 23. SMALL OSCILLATIONS 103 24. BEHAVIOR OF CHARACTERISTIC FREQUENCIES 110 25. PARAMETRIC RESONANCE 113 CHAPTER 6 RIGID BODIES 123 26. MOTION IN A MOVING COORDINATE SYSTEM 123 27. INERTIAL FORCES AND THE CORIOLIS FORCE 129 28. RIGID BODIES 133 29. EULER S EQUATIONS. POINSOT S DESCRIPTION OF THE MOTION 142 30. LAGRANGE S TOP 148 31. SLEEPING TOPS AND FAST TOPS 154 PART III HAMILTONIAN MECHANICS 161 CHAPTER 7 DIFFERENTIAL FORMS 163 32. EXTERIOR FORMS 163 33. EXTERIOR MULTIPLICATION 170 34. DIFFERENTIAL FORMS 174 35. INTEGRATION OF DIFFERENTIAL FORMS 181 36. EXTERIOR DIFFERENTIATION 188 CHAPTER 8 SYMPLECTIC MANIFOLDS 201 37. SYMPLECTIC STRUCTURES ON MANIFOLDS 201 38. HAMILTON IAN PHASE FLOWS AND THEIR INTEGRAL INVARIANTS 204 39. THE LIE ALGEBRA OF VECTOR FIELDS 208 40. THE LIE ALGEBRA OF HAMILTONIAN FUNCTIONS 214 CONTENTS 41. SYMPLECTIC GEOMETRY 219 42. PARAMETRIC RESONANCE IN SYSTEMS WITH MANY DEGREES OF FREEDOM 225 43. A SYMPLECTIC ATLAS 229 CHAPTER 9 CANONICAL FORMALISM 233 44. THE INTEGRAL INVARIANT OF POINCARE-CARTAN 233 45. APPLICATIONS OF THE INTEGRAL INVARIANT OF POINCARE-CARTAN 240 46. HUYGENS PRINCIPLE 248 47. THE HAMILTON-JACOBI METHOD FOR INTEGRATING HAMILTON S CANONICAL EQUATIONS 258 48. GENERATING FUNCTIONS 266 CHAPTER 10 INTRODUCTION TO PERTURBATION THEORY 271 49. INTEGRABLE SYSTEMS 271 50. ACTION-ANGLE VARIABLES 279 51. AVERAGING 285 52. AVERAGING OF PERTURBATIONS 291 APPENDIX 1 RIEMANNIAN CURVATURE 301 APPENDIX 2 GEODESIES OF LEFT-INVARIANT METRICS ON LIE GROUPS AND THE HYDRODYNAMICS OF IDEAL FLUIDS 318 APPENDIX 3 SYMPLECTIC STRUCTURES ON ALGEBRAIC MANIFOLDS 343 APPENDIX 4 CONTACT STRUCTURES 349 APPENDIX 5 DYNAMICAL SYSTEMS WITH SYMMETRIES 371 APPENDIX 6 NORMAL FORMS OF QUADRATIC HAMILTONIANS 381 APPENDIX 7 NORMAL FORMS OF HAMILTONIAN SYSTEMS NEAR STATIONARY POINTS AND CLOSED TRAJECTORIES 385 APPENDIX 8 THEORY OF PERTURBATIONS OF CONDITIONALLY PERIODIC MOTION, AND KOLMOGOROV S THEOREM 399 CONTENTS APPENDIX 9 POINCARE S GEOMETRIC THEOREM, ITS GENERALIZATIONS AND APPLICATIONS 416 APPENDIX 10 MULTIPLICITIES OF CHARACTERISTIC FREQUENCIES, AND ELLIPSOIDS DEPENDING ON PARAMETERS 425 APPENDIX 11 SHORT WAVE ASYMPTOTICS 438 * APPENDIX 12 LAGRANGIAN SINGULARITIES 446 APPENDIX 13 THE KORTEWEG-DE VRIES EQUATION 453 APPENDIX 14 POISSON STRUCTURES 456 APPENDIX 15 ON ELLIPTIC COORDINATES 469 APPENDIX 16 SINGULARITIES OF RAY SYSTEMS 480 INDEX 511
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author	Arnolʹd, V. I. 1937-2010
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isbn	3540968903 0387968903
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-001239110
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physical	IX, 508 S. Ill., zahlr. graph. Darst.
publishDate	1989
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publisher	Springer
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series	Graduate texts in mathematics
series2	Graduate texts in mathematics
spellingShingle	Arnolʹd, V. I. 1937-2010 Mathematical methods of classical mechanics Graduate texts in mathematics Mekanik, Analitik Mécanique analytique Mécanique analytique ram Mechanics, Analytic Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd
subject_GND	(DE-588)4038168-7 (DE-588)4185100-6 (DE-588)4037944-9 (DE-588)4155620-3 (DE-588)4037952-8
title	Mathematical methods of classical mechanics
title_alt	Matematičeskie metody klassičeskoj mechaniki
title_auth	Mathematical methods of classical mechanics
title_exact_search	Mathematical methods of classical mechanics
title_full	Mathematical methods of classical mechanics V. I. Arnold
title_fullStr	Mathematical methods of classical mechanics V. I. Arnold
title_full_unstemmed	Mathematical methods of classical mechanics V. I. Arnold
title_short	Mathematical methods of classical mechanics
title_sort	mathematical methods of classical mechanics
topic	Mekanik, Analitik Mécanique analytique Mécanique analytique ram Mechanics, Analytic Mechanik (DE-588)4038168-7 gnd Theoretische Mechanik (DE-588)4185100-6 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Methode (DE-588)4155620-3 gnd Mathematische Physik (DE-588)4037952-8 gnd
topic_facet	Mekanik, Analitik Mécanique analytique Mechanics, Analytic Mechanik Theoretische Mechanik Mathematik Mathematische Methode Mathematische Physik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001239110&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT arnolʹdvi matematiceskiemetodyklassiceskojmechaniki AT arnolʹdvi mathematicalmethodsofclassicalmechanics

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