Classical and celestial mechanics: the Recife lectures
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2002
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xviii, 385 S. Ill., graph. Darst. |
| ISBN: | 0691050228 |
Staff View
MARC
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| 245 | 1 | 0 | |a Classical and celestial mechanics |b the Recife lectures |c ed. by Hildeberto Cabral ... |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2002 | |
| 300 | |a xviii, 385 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Mecânica celeste |2 larpcal | |
| 650 | 4 | |a Celestial mechanics | |
| 650 | 4 | |a Many-body problem | |
| 650 | 4 | |a Mechanics | |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Himmelsmechanik |0 (DE-588)4127484-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Cabral, Hildeberto |d 1940- |e Sonstige |0 (DE-588)172013526 |4 oth | |
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Record in the Search Index
| _version_ | 1804132963790618624 |
|---|---|
| adam_text | Contents
Foreword xiii
Preface xvii
• Central Configurations and Relative
Equilibria for the Af Body Problem
Dieter Schmidt 1
1 Introduction 2
2 Dziobek s Coordinates 4
3 Configurations for the Three Body Problem 5
4 Configurations in the Four Body Problem 8
5 Configurations in the Five Body Problem 15
6 Palmore s Coordinates 18
APPENDIX A: The Area of a Triangle 26
APPENDIX B: Mathematica Code for the Four Body
Problem 29
APPENDIX C: Mathematica Code for the Planar
Five Body Problem 30
References 33
• Singularities of the JV Body Problem
Florin Diacu 35
1 Introduction 36
2 First Integrals 37
3 Singularities 39
vi Contents
4 Collisions 42
5 Pseudocollisions 43
6 Particular Cases 45
7 Clustered Configurations 46
8 Examples of Pseudocollisions 48
9 Relationships between Singularities 48
10 Extensions beyond Collision 50
11 Block Regularization 51
12 The Collision Manifold 54
13 The Case (3 1 56
14 The Case j3 = 1 57
15 The Case (3 1 58
16 Conclusions and Perspectives 59
References 60
• Lectures on the Two Body Problem
Alain Albouy 63
Introduction 64
Lecture 1. Preliminaries 65
Lecture 2. Two Solutions by Reduction 68
Lecture 3. Why Are Keplerian Orbits Closed? 78
Lecture 4. Concerning the Eccentricity Vector 91
Lecture 5. Lambert s Theorem 99
Bibliography and Author Index 112
Contents vii
• Normal Forms of Hamiltonian Systems and
Stability of Equilibria
Hildeberto Eulalio Cabral 117
1 Introduction 118
2 Hamiltonian Systems 118
3 Symplectic Changes of Coordinates and Generating
Functions 122
4 Hamiltonian Flows 126
5 Stability of Equilibria 129
6 Normal Forms 133
7 The Linear Normalization 138
8 Some Stability Results 140
9 The Restricted Three Body Problem 155
10 Deprit Hori s Normalization Scheme.
Proof of Theorem 6.1 160
References 167
• Poincare s Compactification and Applica¬
tions to Celestial Mechanics
Ernesto Perez Chavela 171
1 Introduction 172
2 Poincare Compactification for Polynomial Vector Fields 174
3 Poincare Compactification for Polynomial Hamiltonian
Vector Fields 177
4 Generic Properties 179
viii Contents
5 Behavior at Infinity in the Monomial Case 183
6 The Kepler Problem 185
6.1 The Kepler Problem on the Line 185
6.2 The Kepler Problem in the Plane 187
7 The Poincare Compactiflcation for Homogeneous
Functions 190
8 The Kepler Problem without Regularization 193
8.1 The Kepler Problem on the Line 194
8.2 The Kepler Problem in the Plane 196
9 Hill s Problem 199
References 203
• The Motion of the Moon
Dieter Schmidt 205
1 Remarks about the Accuracy of the Solution 206
2 The Equations of Motion 208
3 The Solution Method 215
4 The Intermediate Orbit 217
5 The Terms of First Order in the Inclination 219
6 Terms at First Order in e 223
APPENDIX A:
Canonical Transformation to Jacobi Coordinates 230
APPENDIX B:
MACSYMA Program for the Intermediate Orbit 233
APPENDIX C:
MACSYMA Program for Inclination 234
Contents ix
APPENDIX D:
MACSYMA Program for First Order Terms in e 235
References 237
• Lectures on Geometrical Methods in
Mechanics
Mark Levi 239
1 Variational Principles:Their Explanation and Applications240
1.1 Explanation of Fermat s Principle 240
1.2 High Frequency Asymptotics: From Waves to Rays 242
1.3 Solving First Order PDEs Using an Optical Analogy .... 243
1.4 From Optics to Mechanics by Bernoulli 246
1.5 The Maupertuis Euler Lagrange Principle 248
1.6 Hamiltonian Mechanics via Optical Motivation 249
2 Geometrical Basics of Optimal Control 252
2.1 Heuristics of the Maximum Principle 252
2.2 A Geometric Derivation of the Euler Lagrange Equations . 256
3 Geometric Phases in Mechanics 258
3.1 A Shopping Cart Problem 258
3.2 The Holonomy of a Bike Wheel 261
3.3 Dual Cones 262
3.4 Proof of the Gauss Bonnet Formula Using Dual Cones . . . 265
3.5 Duality of External and of Internal Billiards on the Sphere . 267
3.6 Geometric Phases in the Motion of Free Rigid Bodies .... 269
3.7 Euler s Equations of Motion: An Instantaneous Derivation . 273
3.8 Fluid in a Tube 275
3.9 A Spherimeter 277
3.10 Optical Fibers 278
References 280
• Momentum Maps and Geometric Phases
Jair Koiller et aJ. 281
Foreword 282
X Contents
Part 1: Overview 284
1 Adiabatic Phases: Overview 284
2 Nonadiabatic Phases of Gyrostats 287
3 Holonomy with Zero Momentum 291
References 296
Part 2: Classical Adiabatic Angles 298
4 Averaging Heuristics 298
5 The Classical Adiabatic Phases 301
6 Pendulum with Slowly Varying Gravity 304
7 Slowly Moving Integrable Mechanical Systems 306
8 Hannay Berry s 1 Form for Moving Systems 307
9 The Main Theorem 310
9.1 Invariance Under a Maximal Torus Tr 311
9.2 Isotropic Oscillator 313
9.3 Foucault s Pendulum Revisited 314
10 Final Remarks 314
References 315
Part 3: Holonomy for Gyrostats 317
11 The Hamiltonian 317
12 Derivation of Formula (14) 319
12.1 Where and What to Integrate? 320
12.2 Applying Stokes s Theorem 320
12.3 Line Integral over d 321
12.4 Line Integral over C2 321
12.5 The Surface Integral over E 321
13 Holonomy for the Gyrostat 321
Contents xi
14 Final Remarks 322
15 Derivation of the Hamiltonian 323
References 327
Part 4: Microswimming 329
16 Historical Remarks 330
17 The Configuration Space 331
18 Hydrodynamics 333
19 The Momentum Mapping 334
20 Swimming = Holonomy 340
21 Nonspherical Self Reparametrizing Cells 341
21.1 Prolate and Oblate Spheroids 342
21.2 Outline of the Calculation 343
21.3 Results for Prolate and Oblate Spheroids 345
21.4 Comparisons of Swimming Velocities 347
22 Final Remarks 348
References 348
• Bifurcation from Families of Periodic
Solutions
Jack K. Hale and Placido Taboas 351
1 Introduction 352
2 The Alternative Method 353
3 Bifurcation near Families of Solutions 356
3.1 Interaction of Forcing and Damping in a Nonlinear Oscillator 360
3.2 The Predator Prey Model of Lotka Volterra with Periodic
Forcing 373
References 381
Index 383
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Physik Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:01:10Z |
| institution | BVB |
| isbn | 0691050228 |
| language | English |
| lccn | 2002072263 |
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| physical | xviii, 385 S. Ill., graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Princeton Univ. Press |
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| spelling | Classical and celestial mechanics the Recife lectures ed. by Hildeberto Cabral ... Princeton [u.a.] Princeton Univ. Press 2002 xviii, 385 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mecânica celeste larpcal Celestial mechanics Many-body problem Mechanics Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 gnd rswk-swf Himmelsmechanik (DE-588)4127484-2 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Cabral, Hildeberto 1940- Sonstige (DE-588)172013526 oth http://www.loc.gov/catdir/description/prin022/2002072263.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012936084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Classical and celestial mechanics the Recife lectures Mecânica celeste larpcal Celestial mechanics Many-body problem Mechanics Mathematisches Modell (DE-588)4114528-8 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4127484-2 |
| title | Classical and celestial mechanics the Recife lectures |
| title_auth | Classical and celestial mechanics the Recife lectures |
| title_exact_search | Classical and celestial mechanics the Recife lectures |
| title_full | Classical and celestial mechanics the Recife lectures ed. by Hildeberto Cabral ... |
| title_fullStr | Classical and celestial mechanics the Recife lectures ed. by Hildeberto Cabral ... |
| title_full_unstemmed | Classical and celestial mechanics the Recife lectures ed. by Hildeberto Cabral ... |
| title_short | Classical and celestial mechanics |
| title_sort | classical and celestial mechanics the recife lectures |
| title_sub | the Recife lectures |
| topic | Mecânica celeste larpcal Celestial mechanics Many-body problem Mechanics Mathematisches Modell (DE-588)4114528-8 gnd Himmelsmechanik (DE-588)4127484-2 gnd |
| topic_facet | Mecânica celeste Celestial mechanics Many-body problem Mechanics Mathematisches Modell Himmelsmechanik |
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