Chaotic dynamics in Hamiltonian systems: with applications to celestial mechanics
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1997
|
| Series: | [World scientific series on nonlinear science / A]
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 209 S. Ill., graph. Darst. |
| ISBN: | 9810232217 |
Staff View
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Record in the Search Index
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| adam_text | I-. »* WORLD SCIENTIFIC SERIES ON R $ E*»»S» A IUI NE / NONLINEAR
SCIENCE * SENES A VOL 25 SERIES EDITOR: LEON 0. CHUA MUTTONIRN SYSTEMS
WITH APPLICATIONS TO CELESTIAL MECHANICS HARRY DANKOWICZ DEPARTMENT OF
MECHANICS ROYAL INSTITUTE OF TECHNOLOGY STOCKHOLM, SWEDEN WORLD
SCIENTIFIC SINGAPORE * NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE
VII 1 INTRODUCTION 1 1.1 DYNAMICAL SYSTEMS 5 1.1.1 GENERAL TERMINOLOGY 5
1.1.2 FLOWS AND INVARIANT SETS 12 1.1.3 STATIONARY POINTS AND THEIR
STABILITY 17 1.1.4 THE STABLE AND UNSTABLE MANIFOLDS 22 1.1.5 CONSERVED
QUANTITIES 30 1.2 HAMILTONIAN SYSTEMS 32 1.2.1 THE EQUATIONS OF MOTION
32 1.2.2 STABILITY OF STATIONARY POINTS 36 1.3 CLASSICAL MECHANICS 38
1.4 CELESTIAL MECHANICS 40 1.5 NOTES AND REFERENCES 46 2 HAMILTONIAN
SYSTEMS 49 2.1 INVARIANTS 50 2.1.1 POISSON BRACKETS 51 -2.1.2 THE
COMMUTATOR 52 2.1.3 SEPARABILITY 54 2.2 CANONICAL TRANSFORMATIONS 57
2.2.1 THE POISSON BRACKET CONDITIONS 57 2.2.2 MIXED VARIABLE GENERATING
FUNCTIONS 58 2.2.3 SCALING THE INDEPENDENT AND DEPENDENT VARIABLES 62
2.3 INTEGRABILITY VERSUS NONINTEGRABILITY 64 2.4 THE KAM THEOREM 68
2.4.1 FORMAL INTEGRABILITY 68 2.4.2 QUESTIONS OF CONVERGENCE 70 2.4.3
DYNAMICAL CONSEQUENCES 74 2.5 NOTES AND REFERENCES 76 CONTENTS
HOMOCLINIC ORBITS 77 3.1 GENERAL CHARACTERISTICS 77 3.2 THE BERNOULLI
SHIFT 78 3.2.1 TOPOLOGY 79 3.2.2 DYNAMICS 82 3.2.3 IMPLICATIONS 83 3.3
EXPONENTIAL SPLITTING 85 3.3.1 DEFINITIONS AND PROPERTIES 85 3.3.2
SHADOWING ORBITS 92 3.4 TRANSVERSAL INTERSECTIONS 94 3.5 LIAPUNOV
EXPONENTS 98 3.6 NOTES AND REFERENCES 101 THE PERTURBATION APPROACH 103
4.1 DETECTING TRANSVERSAL INTERSECTIONS 104 4.1.1 GENERAL PROPERTIES 104
4.1.2 SOLVING THE VARIATIONAL EQUATIONS 108 4.1.3 SEPARATION OF THE
MANIFOLDS 110 4.2 A RELEVANT SAMPLE PROBLEM 114 4.2.1 THE FIRST
VARIATIONAL EQUATION 116 4.2.2 SECOND-ORDER CALCULATIONS 117 4.3
EVALUATING THE LOWEST-ORDER SEPARATION 118 4.4 NOTES AND REFERENCES 120
APPLICATION - RADIATION PRESSURE I 123 5.1 PHYSICAL CONSIDERATIONS 124
5.1.1 COMMON SOLAR SYSTEM PERTURBATIONS 124 5.1.2 THE BODIES OF THE
SOLAR SYSTEM 131 5.2 THE PLANAR TWO-BODY PROBLEM WITH RADIATION PRESSURE
133 5.2.1 THE PHYSICAL MODEL 133 5.2.2 A MATHEMATICAL FORMULATION 134
5.2.3 THE UNPERTURBED FLOW 135 5.2.4 REDUCTION OF ORDER 139 5.2.5
FIRST-ORDER SEPARATION 140 5.2.6 SECOND-ORDER CALCULATIONS 141 5.3
SOME NUMERICAL RESULTS 142 5.4 NOTES AND REFERENCES 144 GEOMETRY AND
DYNAMICS IN MANY DEGREES OF FREEDOM 145 6.1 GENERAL SETUP 146 6.2 A
RAPID CONVERGENCE SCHEME 148 6.2.1 TOPOLOGY 148 6.2.2 CANONICAL
TRANSFORMATIONS 150 CONTENTS XIII 6.2.3 DYNAMICS 152 6.2.4 THE
GENERATING FUNCTION 155 6.2.5. IMPLICATIONS 160 6.3 GENERAL CONCLUSIONS
161 6.4 THE PERTURBATION APPROACH 163 6.4.1 THE ANSATZ 163 6.4.2 THE
VARIATIONAL EQUATION 164 6.4.3 THE STABLE AND UNSTABLE MANIFOLDS 166 6.5
THE MANIFOLD SEPARATION 170 6.6 CONSEQUENCES OF TRANSVERSAL
INTERSECTIONS - ARNOLD DIFFUSION 172 6.6.1 A SPECIAL CASE OF ARNOLD S
EXAMPLE 172 6.6.2 TRANSITION CHAINS IN ARBITRARY APPLICATIONS 175 6.7
NOTES AND REFERENCES 176 7 APPLICATION - RADIATION PRESSURE II 179 7.1
THE CANONICAL KUSTAANHEIMO-STIEFEL TRANSFORMATION 180 7.2 THE
PHOTO-GRAVITATIONAL THREE-BODY PROBLEM 184 7.3 IN THE ABSENCE OF
ROTATION 188 7.4 IN THE PRESENCE OF ROTATION 193 7.5 THE MANIFOLD
SEPARATION 194 7.6 ARNOLD DIFFUSION 198 7.7 PERSPECTIVE 200 7.8 NOTES
AND REFERENCES 201 OUTLOOK 203 INDEX 207
|
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| indexdate | 2024-07-09T18:28:45Z |
| institution | BVB |
| isbn | 9810232217 |
| language | English |
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| physical | XIII, 209 S. Ill., graph. Darst. |
| publishDate | 1997 |
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| series2 | [World scientific series on nonlinear science / A] |
| spelling | Dankowicz, Harry Verfasser aut Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics Harry Dankowicz Singapore [u.a.] World Scientific 1997 XIII, 209 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier [World scientific series on nonlinear science / A] 25 Chaos Mécanique céleste Mécanique céleste ram Système hamiltonian Celestial mechanics Chaotic behavior in systems Hamiltonian systems Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Chaotisches System (DE-588)4316104-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 s Hamiltonsches System (DE-588)4139943-2 s Chaotisches System (DE-588)4316104-2 s DE-604 A] [World scientific series on nonlinear science 25 (DE-604)BV009051753 25 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008488308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dankowicz, Harry Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics Chaos Mécanique céleste Mécanique céleste ram Système hamiltonian Celestial mechanics Chaotic behavior in systems Hamiltonian systems Himmelsmechanik (DE-588)4127484-2 gnd Chaotisches System (DE-588)4316104-2 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4127484-2 (DE-588)4316104-2 (DE-588)4139943-2 |
| title | Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics |
| title_auth | Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics |
| title_exact_search | Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics |
| title_full | Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics Harry Dankowicz |
| title_fullStr | Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics Harry Dankowicz |
| title_full_unstemmed | Chaotic dynamics in Hamiltonian systems with applications to celestial mechanics Harry Dankowicz |
| title_short | Chaotic dynamics in Hamiltonian systems |
| title_sort | chaotic dynamics in hamiltonian systems with applications to celestial mechanics |
| title_sub | with applications to celestial mechanics |
| topic | Chaos Mécanique céleste Mécanique céleste ram Système hamiltonian Celestial mechanics Chaotic behavior in systems Hamiltonian systems Himmelsmechanik (DE-588)4127484-2 gnd Chaotisches System (DE-588)4316104-2 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Chaos Mécanique céleste Système hamiltonian Celestial mechanics Chaotic behavior in systems Hamiltonian systems Himmelsmechanik Chaotisches System Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008488308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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