Mechanics: an intensive course
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2012
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XVII, 468 S. graph. Darst. |
| ISBN: | 9783642163906 |
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Record in the Search Index
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| adam_text |
IMAGE 1
CONTENTS
1 FOUNDATIONS OF NEWTONIAN MECHANICS 1
1.1 NOTIONS, PRINCIPLES AND FUNDAMENTAL THEOREMS OF NEWTONIAN MECHANICS
1
1.1.1 VELOCITY. ACCELERATION 2
1.1.2 ANALYTICAL EXPRESSIONS FOR VELOCITY AND ACCELERATION IN DIFFERENT
COORDINATE SYSTEMS 4
1.2 PRINCIPLES OF NEWTONIAN MECHANICS 6
1.2.1 THE PRINCIPLE OF INERTIA (NEWTON'S FIRST LAW) 6
1.2.2 THE LAW OF FORCE (NEWTON'S SECOND LAW) 7
1.2.3 THE PRINCIPLE OF ACTION AND REACTION (NEWTON'S THIRD LAW) 8
1.3 GENERAL THEOREMS OF NEWTONIAN MECHANICS 9
1.3.1 INTEGRATION OF THE EQUATIONS OF MOTION 9
1.3.2 FIRST INTEGRALS 11
1.3.3 GENERAL THEOREMS OF ONE-PARTICLE MECHANICS 12 1.3.4 GENERAL
THEOREMS FOR SYSTEMS OF PARTICLES 15
1.4 PROBLEMS 23
2 PRINCIPLES OF ANALYTICAL MECHANICS 27
2.1 CONSTRAINTS 27
2.1.1 ONE-PARTICLE SYSTEMS 27
2.1.2 MANY-PARTICLE SYSTEMS 39
2.2 ELEMENTARY DISPLACEMENTS 40
2.3 PRINCIPLE OF VIRTUAL WORK 42
2.3.1 FREE PARTICLE 42
2.3.2 PARTICLE SUBJECT TO CONSTRAINTS 42
2.3.3 SYSTEM OF FREE PARTICLES 43
2.3.4 SYSTEM OF PARTICLES SUBJECT TO CONSTRAINTS 43
2.3.5 APPLICATION 46
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1006644903
DIGITALISIERT DURCH
IMAGE 2
XIV CONTENTS
2.4 GENERALIZED COORDINATES 47
2.4.1 CONFIGURATION SPACE 48
2.4.2 GENERALIZED FORCES 49
2.4.3 KINETIC ENERGY IN GENERALIZED COORDINATES 51
2.5 DIFFERENTIAL AND INTEGRAL PRINCIPLES IN ANALYTICAL MECHANICS . . 52
2.5.1 D'ALEMBERT'S PRINCIPLE 53
2.5.2 LAGRANGE EQUATIONS FOR HOLONOMIC SYSTEMS 53
2.5.3 VELOCITY-DEPENDENT POTENTIAL 57
2.5.4 NON-POTENTIAL FORCES 60
2.6 ELEMENTS OF CALCULUS OF VARIATIONS 62
2.6.1 SHORTEST DISTANCE BETWEEN TWO POINTS IN A PLANE . . . 66 2.6.2
BRACHISTOCHRONE PROBLEM 67
2.6.3 SURFACE OF REVOLUTION OF MINIMUM AREA 68
2.6.4 GEODESIES 69
2.7 HAMILTON'S PRINCIPLE 74
2.7.1 EULER-LAGRANGE EQUATIONS FOR THE ACTION INTEGRAL . . . 77 2.7.2
CRITERIA FOR THE CONSTRUCTION OF LAGRANGIANS 79
2.8 SYMMETRY PROPERTIES AND CONSERVATION THEOREMS 79
2.8.1 FIRST INTEGRALS AS CONSTANTS OF MOTION 80
2.8.2 SYMMETRY TRANSFORMATIONS 82
2.8.3 NOETHER'S THEOREM 82
2.9 PRINCIPLE OF LEAST ACTION 86
2.10 PROBLEMS 93
3 APPLICATIONS OF THE LAGRANGIAN FORMALISM IN THE STUDY OF DISCRETE
PARTICLE SYSTEMS 97
3.1 CENTRAL FORCE FIELDS 97
3.1.1 TWO-BODY PROBLEM 97
3.1.2 GENERAL PROPERTIES OF MOTION IN CENTRAL FIELD 99
3.1.3 DISCUSSION OF TRAJECTORIES 101
3.1.4 BERTRAND'S THEOREM 105
3.2 KEPLER'S PROBLEM 108
3.2.1 DETERMINATION OF TRAJECTORIES 109
3.2.2 LAW OF MOTION 113
3.2.3 RUNGE-LENZ VECTOR 116
3.2.4 ARTIFICIAL SATELLITES OF THE EARTH. COSMIC VELOCITIES . . 118 3.3
CLASSICAL THEORY OF COLLISIONS BETWEEN PARTICLES 121
3.3.1 COLLISIONS BETWEEN TWO PARTICLES 121
3.3.2 EFFECTIVE SCATTERING CROSS SECTION 125
3.3.3 SCATTERING ON A SPHERICAL POTENTIAL WELL 129
3.3.4 RUTHERFORD'S FORMULA 131
3.4 PERIODICAL MOTION OF A PARTICLE UNDER THE INFLUENCE OF GRAVITY . .
132 3.4.1 SIMPLE PENDULUM 133
3.4.2 CYCLOIDAL PENDULUM 136
3.4.3 SPHERICAL PENDULUM 137
IMAGE 3
CONTENTS XV
3.5 MOTION OF A PARTICLE SUBJECT TO AN ELASTIC FORCE 140
3.5.1 HARMONIC LINEAR OSCILLATOR 140
3.5.2 SPACE OSCILLATOR 141
3.5.3 NON-LINEAR OSCILLATIONS 143
3.6 SMALL OSCILLATIONS ABOUT A POSITION OF STABLE EQUILIBRIUM . . . 144
3.6.1 EQUATIONS OF MOTION. NORMAL COORDINATES 146
3.6.2 SMALL OSCILLATIONS OF MOLECULES 149
3.7 ANALOGY BETWEEN MECHANICAL AND ELECTRIC SYSTEMS 153 3.7.1 KIRCHHOFF
S RULE RELATIVE TO THE LOOPS OF AN ELECTRIC CIRCUIT 153
3.7.2 KIRCHHOFF S RULE RELATIVE TO THE JUNCTION POINTS OF AN ELECTRIC
CIRCUIT 157
3.8 PROBLEMS 159
4 RIGID BODY MECHANICS 163
4.1 GENERAL CONSIDERATIONS 163
4.2 DISTRIBUTION OF VELOCITIES AND ACCELERATIONS IN A RIGID BODY . .
165 4.3 INERTIAL FORCES 168
4.3.1 ACTION OF THE CORIOLIS FORCE ON THE MOTION OF BODIES AT THE
SURFACE OF THE EARTH 170
4.3.2 FOUCAULT'S PENDULUM 172
4.4 EULER'S ANGLES 175
4.5 MOTION OF A RIGID BODY ABOUT A FIXED POINT 177
4.5.1 KINEMATIC PRELIMINARIES 178
4.5.2 ANGULAR MOMENTUM 179
4.5.3 KINETIC ENERGY 180
4.5.4 ELLIPSOID OF INERTIA 182
4.5.5 EULER'S EQUATIONS OF MOTION 183
4.6 APPLICATIONS 188
4.6.1 PHYSICAL PENDULUM 188
4.6.2 SYMMETRICAL TOP 189
4.6.3 FAST TOP. THE GYROSCOPE 197
4.6.4 MOTION OF A RIGID BODY RELATIVE TO A NON-INERTIAL FRAME. THE
GYROCOMPASS 198
4.6.5 MOTION OF RIGID BODIES IN CONTACT 202
4.6.6 MECHANICAL-ELECTROMAGNETIC ANALOGIES 205
4.7 PROBLEMS 208
5 HAMILTONIAN FORMALISM 211
5.1 HAMILTON'S CANONICAL EQUATIONS 211
5.1.1 MOTION OF A PARTICLE IN A PLANE 216
5.1.2 MOTION OF A PARTICLE RELATIVE TO A NON-INERTIAL FRAME . 218 5.1.3
MOTION OF A CHARGED PARTICLE IN AN ELECTROMAGNETIC FIELD 219
5.1.4 ENERGY OF A MAGNETIC DIPOLE IN AN EXTERNAL F I E L D . . . 222
IMAGE 4
CONTENTS
5.2 ROUTH'S EQUATIONS 222
5.3 POISSON BRACKETS 225
5.3.1 POISSON BRACKETS FOR ANGULAR MOMENTUM 228
5.3.2 POISSON BRACKETS AND COMMUTATORS 231
5.3.3 LAGRANGE BRACKETS 234
5.4 CANONICAL TRANSFORMATIONS 236
5.4.1 EXTENSIONS AND APPLICATIONS 241
5.4.2 MECHANICAL-THERMODYNAMICAL ANALOGY. THERMODYNAMIC POTENTIALS 247
5.5 INFINITESIMAL CANONICAL TRANSFORMATIONS 249
5.5.1 TOTAL MOMENTUM AS GENERATOR OF TRANSLATIONS 251 5.5.2 TOTAL
ANGULAR MOMENTUM AS GENERATOR OF ROTATIONS 251
5.5.3 HAMILTONIAN AS GENERATOR OF TIME-EVOLUTION 252 5.6 INTEGRAL
INVARIANTS 253
5.6.1 INTEGRAL INVARIANTS OF THE CANONICAL EQUATIONS 255 5.6.2 THE
RELATIVE UNIVERSAL INVARIANT OF MECHANICS 256 5.6.3 LIOUVILLE'S THEOREM
258
5.6.4 PFAFF FORMS 261
5.6.5 QUANTUM MECHANICAL HARMONIC OSCILLATOR 263
5.7 HAMILTON-JACOBI FORMALISM 265
5.7.1 HAMILTON-JACOBI EQUATION 265
5.7.2 METHODS FOR SOLVING THE HAMILTON-JACOBI EQUATION. . . 268 5.7.3
APPLICATIONS 273
5.7.4 ACTION-ANGLE VARIABLES 278
5.7.5 ADIABATIC INVARIANTS 287
5.8 PROBLEMS 289
MECHANICS OF CONTINUOUS DEFORMABLE MEDIA 293
6.1 GENERAL CONSIDERATIONS 293
6.2 KINEMATICS OF CONTINUOUS DEFORMABLE MEDIA 294
6.2.1 LAGRANGE'S METHOD 294
6.2.2 EULER'S METHOD 295
6.3 DYNAMICS OF CONTINUOUS MEDIA 297
6.3.1 EQUATION OF CONTINUITY 297
6.3.2 FORCES ACTING UPON A CONTINUOUS DEFORMABLE MEDIUM 300
6.3.3 GENERAL THEOREMS 301
6.3.4 EQUATIONS OF MOTION OF A CDM. CAUCHY STRESS TENSOR 302
6.4 DEFORMATION OF A CONTINUOUS DEFORMABLE MEDIUM ABOUT A POINT. LINEAR
APPROXIMATION 306
6.4.1 ROTATION TENSOR AND SMALL-STRAIN TENSOR 306
6.4.2 SAINT-VENANT COMPATIBILITY CONDITIONS 309
6.4.3 FINITE-STRAIN TENSOR 310
IMAGE 5
CONTENTS XVII
6.5 ELASTIC MEDIUM 311
6.5.1 HOOKE'S GENERALIZED LAW 311
6.5.2 EQUATIONS OF MOTION OF AN ELASTIC MEDIUM 315
6.5.3 PLANE WAVES IN ISOTROPIE ELASTIC MEDIA 317
6.6 PERFECT FLUID 319
6.6.1 EQUATION OF MOTION OF A PERFECT HUID 319
6.6.2 PARTICULAR TYPES OF MOTION OF AN IDEAL FLUID 320
6.6.3 FUNDAMENTAL CONSERVATION THEOREMS 328
6.6.4 MAGNETODYNAMICS OF IDEAL FLUIDS 338
6.7 VISCOUS FLUID 339
6.8 LAGRANGIAN FORMALISM 344
6.8.1 EULER-LAGRANGE EQUATIONS FOR CONTINUOUS SYSTEMS . . . 344 6.8.2
APPLICATIONS 347
6.9 HAMILTONIAN FORMALISM 357
6.9.1 HAMILTON'S CANONICAL EQUATIONS FOR CONTINUOUS SYSTEMS 357
6.9.2 APPLICATIONS 362
6.10 NOETHER'S THEOREM FOR CONTINUOUS SYSTEMS 373
6.10.1 HAMILTON'S PRINCIPLE AND THE EQUATIONS OF MOTION. . . 373 6.10.2
SYMMETRY TRANSFORMATIONS 377
6.10.3 ENERGY CONSERVATION THEOREM 380
6.10.4 MOMENTUM CONSERVATION THEOREM 381
6.10.5 ANGULAR MOMENTUM CONSERVATION THEOREM 382 6.10.6 CENTRE OF MASS
THEOREM 383
6.11 PROBLEMS 385
ADDENDA 387
ADDENDUM I: SPECIAL THEORY OF RELATIVITY 389
ADDENDUM II: QUANTUM THEORY AND THE ATOM 399
ADDENDUM III: STOCHASTIC PROCESSES AND THE LANGEVIN EQUATION 409
APPENDIX A: ELEMENTS OF VECTOR AND TENSOR ALGEBRA 411
APPENDIX B: ELEMENTS OF VECTOR AND TENSOR ANALYSIS 427
REFERENCES 447
AUTHOR INDEX 449
SUBJECT INDEX 451 |
| any_adam_object | 1 |
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| dewey-ones | 531 - Classical mechanics |
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| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| spelling | Chaichian, Masud 1941- Verfasser (DE-588)135881072 aut Mechanics an intensive course Masud Chaichian ; Ioan Merches ; Anca Tureanu Berlin [u.a.] Springer 2012 XVII, 468 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mechanik (DE-588)4038168-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mechanik (DE-588)4038168-7 s DE-604 Mercheş, Ioan 1937- Verfasser (DE-588)1019621214 aut Tureanu, Anca Verfasser (DE-588)1019621397 aut Erscheint auch als Online-Ausgabe 978-3-642-17234-2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3534018&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022481056&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chaichian, Masud 1941- Mercheş, Ioan 1937- Tureanu, Anca Mechanics an intensive course Mechanik (DE-588)4038168-7 gnd |
| subject_GND | (DE-588)4038168-7 (DE-588)4123623-3 |
| title | Mechanics an intensive course |
| title_auth | Mechanics an intensive course |
| title_exact_search | Mechanics an intensive course |
| title_full | Mechanics an intensive course Masud Chaichian ; Ioan Merches ; Anca Tureanu |
| title_fullStr | Mechanics an intensive course Masud Chaichian ; Ioan Merches ; Anca Tureanu |
| title_full_unstemmed | Mechanics an intensive course Masud Chaichian ; Ioan Merches ; Anca Tureanu |
| title_short | Mechanics |
| title_sort | mechanics an intensive course |
| title_sub | an intensive course |
| topic | Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Mechanik Lehrbuch |
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