| 000 | 10181cam a22003137a 4500 | ||
|---|---|---|---|
| 003 | CUTN | ||
| 005 | 20250328150700.0 | ||
| 008 | 100909s2011 gw a b 001 0 eng d | ||
| 020 | _a9783662601310 (alk. paper) | ||
| 041 | _aEnglish | ||
| 042 | _alccopycat | ||
| 082 | 0 | 0 |
_a531.015 _223 _bDRE |
| 100 | 1 | _aDreizler, Reiner M. | |
| 245 | 1 | 0 |
_aTheoretical physics. _cReiner M. Dreizler, Cora S. Lüdde. |
| 245 | 1 | 0 |
_n1 _pTheoretical mechanics / |
| 246 | 1 | 0 | _aTheoretical mechanics |
| 250 | _a1st ed. | ||
| 260 |
_aHeidelberg _aNew York : _bSpringer, _cc2010. |
||
| 300 |
_aix, 402 p. : _bill. ; _c24 cm. |
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| 490 | 0 |
_aGraduate texts in physics, _x1868-4513 |
|
| 504 | _aIncludes bibliographical references (p. [353]-356) and index. | ||
| 505 | _t1 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 momentum 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 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 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 coordinate 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 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 . . . . . . . . . . . . . . 373 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 F.1 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 (δ small) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 | ||
| 520 | _aThis book is the first of a series covering the major topics that are taught in university courses in Theoretical Physics: Mechanics, Electrodynamics, Quantum Theory and Statistical Physics. After an introduction to basic concepts of mechanics more advanced topics build the major part of this book. Interspersed is a discussion of selected problems of motion. This is followed by a concise treatment of the Lagrangian and the Hamiltonian formulation of mechanics, as well as a brief excursion on chaotic motion. The last chapter deals with applications of the Lagrangian formulation to specific systems (coupled oscillators, rotating coordinate systems, rigid bodies). The level of the last sections is advanced. The text is accompanied by an extensive collection of online material, in which the possibilities of the electronic medium are fully exploited, e.g. in the form of applets, 2D- and 3D-animations. It contains: A collection of 74 problems with detailed step-by-step guidance towards the solutions, a collection of comments and additional mathematical details in support of the main text, a complete presentation of all the mathematical tools needed. | ||
| 650 | 0 | _aMechanics, Analytic. | |
| 700 | 1 | _aLüdde, Cora S. | |
| 906 |
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| 942 |
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| 999 |
_c44126 _d44126 |
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