Structure and interpretation of classical mechanics:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Mass. [u.a.]
MIT
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 534 S. graph. Darst. |
| ISBN: | 0262194554 9780262194556 |
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| adam_text | STRUCTURE AND INTERPRETATION OF CLASSICAL MECHANICS GERALD JAY SUSSMAN
AND JACK WISDOM WITH MEINHARD E. MAYER THE MIT PRESS CAMBRIDGE,
MASSACHUSETTS LONDON, ENGLAND CONTENTS CONTENTS PREFACE ACKNOWLEDGMENTS
LAGRANGIAN MECHANICS 1.1 1.2 1.3 1.4 1.5 1.5.1 1.5.2 1.6 1.6.1 1.6.2
1.6.3 1.6.4 1.7 1.8 1.8.1 1.8.2 1.8.3 1.8.4 1.9 1.10 THE PRINCIPLE OF
STATIONARY ACTION CONFIGURATION SPACES GENERALIZED COORDINATES COMPUTING
ACTIONS THE EULER-LAGRANGE EQUATIONS DERIVATION OF THE LAGRANGE
EQUATIONS COMPUTING LAGRANGE S EQUATIONS HOW TO FIND LAGRANGIANS
COORDINATE TRANSFORMATIONS SYSTEMS WITH RIGID CONSTRAINTS CONSTRAINTS AS
COORDINATE TRANSFORMATIONS THE LAGRANGIAN IS NOT UNIQUE EVOLUTION OF
DYNAMICAL STATE CONSERVED QUANTITIES CONSERVED MOMENTA ENERGY
CONSERVATION CENTRAL FORCES IN THREE DIMENSIONS NOETHER S THEOREM
ABSTRACTION OF PATH FUNCTIONS CONSTRAINED MOTION 1.10.1 COORDINATE
CONSTRAINTS VII XIII XIX 1 4 9 11 16 26 27 34 37 44 47 59 62 66 74 76 78
80 83 87 92 94 VLLL CONTENTS 1.10.2 DERIVATIVE CONSTRAINTS 101 1.10.3
NONHOLONOMIC SYSTEMS 105 1.11 SUMMARY 108 1.12 PROJECTS 109 2 RIGID
BODIES 113 2.1 ROTATIONAL KINETIC ENERGY 114 2.2 KINEMATICS OF ROTATION
116 2.3 MOMENTS OF INERTIA 118 2.4 INERTIA TENSOR 121 2.5 PRINCIPAL
MOMENTS OF INERTIA 122 2.6 REPRESENTATION OF THE ANGULAR VELOCITY VECTOR
125 2.7 EULER ANGLES 128 2.8 VECTOR ANGULAR MOMENTUM 132 2.9 MOTION OF A
FREE RIGID BODY 134 2.9.1 COMPUTING THE MOTION OF FREE RIGID BODIES 136
2.9.2 QUALITATIVE FEATURES 139 2.10 AXISYMMETRIC TOPS 143 2.11
SPIN-ORBIT COUPLING 151 2.11.1 DEVELOPMENT OF THE POTENTIAL ENERGY 152
2.11.2 ROTATION OF THE MOON AND HYPERION 156 2.12 EULER S EQUATIONS 163
2.13 NONSINGULAR GENERALIZED COORDINATES 168 2.14 SUMMARY 176 2.15
PROJECTS 177 3 HAMILTONIAN MECHANICS 179 3.1 HAMILTON S EQUATIONS 181
3.1.1 THE LEGENDRE TRANSFORMATION 189 3.1.2 HAMILTON S EQUATIONS FROM
THE ACTION PRINCIPLE 199 3.1.3 A WIRING DIAGRAM 201 3.2 POISSON BRACKETS
203 IX 3.3 ONE DEGREE OF PREEDOM 206 3.4 PHASE SPACE REDUCTION 208 3.4.1
LAGRANGIAN REDUCTION 218 3.5 PHASE SPACE EVOLUTION 220 3.5.1 PHASE-SPACE
DESCRIPTION IS NOT UNIQUE 222 3.6 SURFACES OF SECTION 223 3.6.1
PERIODICALLY DRIVEN SYSTEMS 225 3.6.2 COMPUTING STROBOSCOPIC SURFACES OF
SECTION 230 3.6.3 AUTONOMOUS SYSTEMS 232 3.6.4 COMPUTING HENON-HEILES
SURFACES OF SECTION 244 3.6.5 NON-AXISYMMETRIC TOP 245 3.7 EXPONENTIAL
DIVERGENCE 247 3.8 LIOUVILLE S THEOREM 250 3.9 STANDARD MAP 260 3.10
SUMMARY 263 3.11 PROJECTS 264 PHASE SPACE STRUCTURE 267 4.1 EMERGENCE OF
THE DIVIDED PHASE SPACE 268 4.2 LINEAR STABILITY 273 4.2.1 EQUILIBRIA OF
DIFFERENTIAL EQUATIONS 273 4.2.2 FIXED POINTS OF MAPS 277 4.2.3
RELATIONS AMONG EXPONENTS 279 4.3 HOMOCLINIC TANGLE 284 4.3.1
COMPUTATION OF STABLE AND UNSTABLE MANIFOLDS 289 4.4 INTEGRABLE SYSTEMS
292 4.5 POINCARE-BIRKHOFF THEOREM 297 4.5.1 COMPUTING THE
POINCARE-BIRKHOFF CONSTRUCTION 302 4.6 INVARIANT CURVES 303 4.6.1
FINDING INVARIANT CURVES 307 4.6.2 DISSOLUTION OF INVARIANT CURVES 312
4.7 SUMMARY 315 4.8 PROJECTS 317 X CONTENTS CANONICAL TRANSFORMATIONS
5.1 5.2 5.2.1 5.2.2 5.2.3 5.2.4 5.3 5.4 5.4.1 5.5 5.6 5.6.1 5.6.2 5.6.3
5.6.4 5.6.5 5.7 5.7.1 5.7.2 5.8 5.8.1 5.8.2 5.8.3 5.8.4 5.9 5.10 5.11
5.12 5.13 POINT TRANSFORMATIONS GENERAL CANONICAL TRANSFORMATIONS
TIME-INDEPENDENT CANONICAL TRANSFORMATIONS SYMPLECTIC TRANSFORMATIONS
TIME-DEPENDENT TRANSFORMATIONS THE SYMPLECTIC CONDITION INVARIANTS OF
CANONICAL TRANSFORMATIONS EXTENDED PHASE SPACE POINCARE-CARTAN INTEGRAL
INVARIANT REDUCED PHASE SPACE GENERATING FUNCTIONS F GENERATES
CANONICAL TRANSFORMATIONS GENERATING FUNCTIONS AND INTEGRAL INVARIANTS
TYPES OF GENERATING FUNCTIONS POINT TRANSFORMATIONS CLASSICAL GAUGE
TRANSFORMATIONS TIME EVOLUTION IS CANONICAL ANOTHER VIEW OF TIME
EVOLUTION YET ANOTHER VIEW OF TIME EVOLUTION HAMILTON-JACOBI EQUATION
HARMONIE OSCILLATOR KEPLER PROBLEM I*2 AND THE LAGRANGIAN THE ACTION
GENERATES TIME EVOLUTION LIE TRANSFORMS LIE SERIES EXPONENTIAL
IDENTITIES SUMMARY PROJECTS CANONICAL PERTURBATION THEORY 6.1
PERTURBATION THEORY WITH LIE SERIES 319 320 324 327 332 335 338 339 346
354 355 359 362 364 369 371 387 391 397 401 403 405 409 413 415 417 423
431 433 434 439 440 6.2 PENDULUM AS A PERTURBED ROTOR 442 CONTENTS XI
6.2.1 HIGHER ORDER 450 6.2.2 ELIMINATING SECULAR TERMS 453 6.3 MANY
DEGREES OF FREEDOM 455 6.3.1 DRIVEN PENDULUM AS A PERTURBED ROTOR 458
6.4 NONLINEAR RESONANCE 459 6.4.1 PENDULUM APPROXIMATION 461 6.4.2
READING THE HAMILTONIAN 468 6.4.3 RESONANCE-OVERLAP CRITERION 468 6.4.4
HIGHER-ORDER PERTURBATION THEORY 470 6.4.5 STABILITY OF THE INVERTED
VERTICAL EQUILIBRIUM 473 6.5 SUMMARY 476 6.6 PROJECTS 477 7 APPENDIX:
SCHEINE 479 8 APPENDIX: OUR NOTATION 489 REFERENCES 505 LIST OF
EXERCISES 509 INDEX 511
|
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| author | Sussman, Gerald Jay 1947- Wisdom, Jack 1953- Mayer, Meinhard E. 1929-2011 |
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| language | English |
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| spelling | Sussman, Gerald Jay 1947- Verfasser (DE-588)1043872582 aut Structure and interpretation of classical mechanics Gerald Jay Sussmann and Jack Wisdom with Meinhard E. Mayer Cambridge, Mass. [u.a.] MIT 2001 XXI, 534 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Theoretische Mechanik - Lehrbuch Mechanik (DE-588)4038168-7 gnd rswk-swf Mechanik (DE-588)4038168-7 s DE-604 Wisdom, Jack 1953- Verfasser (DE-588)1043873015 aut Mayer, Meinhard E. 1929-2011 Verfasser (DE-588)172273676 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009371921&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sussman, Gerald Jay 1947- Wisdom, Jack 1953- Mayer, Meinhard E. 1929-2011 Structure and interpretation of classical mechanics Theoretische Mechanik - Lehrbuch Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4038168-7 |
| title | Structure and interpretation of classical mechanics |
| title_auth | Structure and interpretation of classical mechanics |
| title_exact_search | Structure and interpretation of classical mechanics |
| title_full | Structure and interpretation of classical mechanics Gerald Jay Sussmann and Jack Wisdom with Meinhard E. Mayer |
| title_fullStr | Structure and interpretation of classical mechanics Gerald Jay Sussmann and Jack Wisdom with Meinhard E. Mayer |
| title_full_unstemmed | Structure and interpretation of classical mechanics Gerald Jay Sussmann and Jack Wisdom with Meinhard E. Mayer |
| title_short | Structure and interpretation of classical mechanics |
| title_sort | structure and interpretation of classical mechanics |
| topic | Theoretische Mechanik - Lehrbuch Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Theoretische Mechanik - Lehrbuch Mechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009371921&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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