Theoretical physics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Heidelberg [u.a.]
Springer
|
| Schriftenreihe: | Graduate texts in physics
|
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
Internformat
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Datensatz im Suchindex
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IMAGE 1
TABLE OF CONTENTS
1 A FIRST SURVEY 1
2 KINEMATICS 13
2.1 ONE-DIMENSIONAL MOTION 13
2.1.1 THREE EXAMPLES FOR THE MOTION IN ONE SPACE DIMENSION 14 2.1.2
VELOCITY 19
2.1.3 ACCELERATION 22
2.1.4 FIRST REMARKS CONCERNING DYNAMICAL ASPECTS 25 2.2 PROBLEMS OF
MOTION IN TWO OR THREE DIMENSIONS 27
2.2.1 TWO-DIMENSIONAL MOTION 29
2.2.2 MOTION IN THREE SPATIAL DIMENSIONS 36
2.2.3 AN EXAMPLE FOR THE DETERMINATION OF TRAJECTORIES IN TWO SPACE
DIMENSIONS 38
2.3 VECTORIAL FORMULATION OF PROBLEMS OF MOTION 40
2.3.1 BASIC CONCEPTS 41
2.3.2 VECTORIAL DESCRIPTION OF MOTION 43
2.3.3 AREA THEOREM 48
2.4 CURVILINEAR COORDINATES 53
2.4.1 COORDINATES IN THE PLANE 53
2.4.2 SPATIAL COORDINATES 60
3 DYNAMICS I: AXIOMS AND CONSERVATION LAWS 67
3.1 THE AXIOMS OF MECHANICS 67
3.1.1 THE CONCEPT OF FORCE 67
3.1.2 INERTIAL AND GRAVITATIONAL MASS 69
3.1.3 THE AXIOMS 72
3.1.4 THE FIRST AXIOM: INERTIAL SYSTEMS 72
3.1.5 THE SECOND AXIOM: MOMENTUM 76
3.1.6 THE THIRD AXIOM: INTERACTIONS 77
3.2 THE CONSERVATION LAWS OF MECHANICS 84
3.2.1 THE MOMENTUM PRINCIPLE AND MOMENTUM CONSERVATION 84 3.2.2 THE
ANGULAR MOMENTUM PRINCIPLE AND ANGULAR MOMEN- TUM CONSERVATION 91
3.2.3 ENERGY AND ENERGY CONSERVATION FOR A MASS POINT 102 3.2.4 ENERGY
CONSERVATION FOR A SYSTEM OF MASS POINTS 122
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000032973
DIGITALISIERT DURCH
IMAGE 2
VIII TABLE OF CONTENTS
3.2.5 APPLICATION: COLLISION PROBLEMS 130
4 DYNAMICS II: PROBLEMS OF MOTION 139
4.1 KEPLER'S PROBLEM 139
4.1.1 PRELIMINARIES 140
4.1.2 PLANETARY MOTION 141
4.1.3 COMETS AND METEORITES 155
4.2 OSCILLATOR PROBLEMS 160
4.2.1 THE MATHEMATICAL PENDULUM 161
4.2.2 THE DAMPED HARMONIC OSCILLATOR 169
4.2.3 FORCED OSCILLATIONS: HARMONIC RESTORING FORCES 173 4.2.4 FORCED
OSCILLATIONS: GENERAL EXCITATIONS 180
5 GENERAL FORMULATION OF THE MECHANICS OF POINT PARTICLES. . 185 5.1
LAGRANGE I: THE LAGRANGE EQUATIONS OF THE FIRST KIND 186 5.1.1 EXAMPLES
FOR THE MOTION UNDER CONSTRAINTS 186
5.1.2 LAGRANGE I FOR ONE POINT PARTICLE 192
5.2 D'ALEMBERT'S PRINCIPLE 204
5.2.1 D'ALEMBERT'S PRINCIPLE FOR ONE MASS POINT 204
5.2.2 D'ALEMBERT'S PRINCIPLE FOR SYSTEMS OF POINT PARTICLES . 209 5.3
THE LAGRANGE EQUATIONS OF THE SECOND KIND (LAGRANGE II) . . 214 5.3.1
LAGRANGE II FOR ONE POINT PARTICLE 214
5.3.2 LAGRANGE II AND CONSERVATION LAWS FOR ONE POINT PARTICLE. 231
5.3.3 LAGRANGE II FOR A SYSTEM OF MASS POINTS 241
5.4 HAMILTON'S FORMULATION OF MECHANICS 246
5.4.1 HAMILTON'S PRINCIPLE 246
5.4.2 HAMILTON'S EQUATION OF MOTION 254
5.4.3 A CURSORY LOOK INTO PHASE SPACE 262
6 APPLICATION OF THE LAGRANGE FORMALISM 271
6.1 COUPLED HARMONIC OSCILLATORS 271
6.1.1 COUPLED OSCILLATING SYSTEM: TWO MASSES AND THREE SPRINGS 272 6.1.2
BEATS 276
6.1.3 THE LINEAR OSCILLATOR CHAIN 278
6.1.4 THE DIFFERENTIAL EQUATION OF AN OSCILLATING STRING 290 6.2
ROTATING COORDINATE SYSTEMS 294
6.2.1 SIMPLE MANIFESTATION OF APPARENT FORCES 295
6.2.2 GENERAL DISCUSSION OF APPARENT FORCES IN ROTATING COOR- DINATE
SYSTEMS 297
6.2.3 APPARENT FORCES AND THE ROTATING EARTH 305
6.3 THE MOTION OF RIGID BODIES 314
6.3.1 PRELIMINARIES 315
6.3.2 THE KINETIC ENERGY OF RIGID BODIES 316
6.3.3 THE STRUCTURE OF THE INERTIA MATRIX 322
6.3.4 THE ANGULAR MOMENTUM OF A RIGID BODY 332
IMAGE 3
TABLE OF CONTENTS IX
6.3.5 THE EULER ANGLES 334
6.3.6 THE EQUATIONS OF MOTION FOR THE ROTATION OF A RIGID BODY 337 6.3.7
ROTATIONAL MOTION OF RIGID BODIES 340
REFERENCES 353
APPENDIX 357
A BIOGRAPHICAL DATA 359
B THE GREEK ALPHABET 365
C NOMENCLATURE 367
D PHYSICAL QUANTITIES 369
E SOME CONSTANTS AND ASTRONOMICAL DATA 373
F FORMULAE 377
F.I PLANE POLAR COORDINATES 377
F.2 CYLINDER COORDINATES 378
F.3 SPHERICAL COORDINATES 378
F.4 SUM FORMULAE / MOIVRE FORMULA 379
F.5 HYPERBOLIC FUNCTIONS 380
F.6 SERIES EXPANSIONS 380
F.7 APPROXIMATIONS (6 SMALL) 380
G PROBLEMS ON THE VIRTUAL CD-ROM 381
INDEX 397 |
| any_adam_object | 1 |
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| author_sort | Dreizler, Reiner M. 1936- |
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| building | Verbundindex |
| bvnumber | BV036803697 |
| ctrlnum | (DE-599)DNB1000032973 |
| discipline | Geographie |
| format | Book |
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| spellingShingle | Dreizler, Reiner M. 1936- Lüdde, Cora S. Theoretical physics |
| title | Theoretical physics |
| title_auth | Theoretical physics |
| title_exact_search | Theoretical physics |
| title_full | Theoretical physics Reiner M. Dreizler ; Cora S. Lüdde |
| title_fullStr | Theoretical physics Reiner M. Dreizler ; Cora S. Lüdde |
| title_full_unstemmed | Theoretical physics Reiner M. Dreizler ; Cora S. Lüdde |
| title_short | Theoretical physics |
| title_sort | theoretical physics |
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