Modern classical mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2021
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xix, 687 Seiten Illustrationen, Diagramme |
| ISBN: | 9781108834971 |
Internformat
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| 245 | 1 | 0 | |a Modern classical mechanics |c T.M. Helliwell, Harvey Mudd College, California, V.V. Sahakian, Harvey Mudd College, California |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2021 | |
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Datensatz im Suchindex
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| adam_text | ям Contents Preface Acknowledgments and Credits Notation and Conventions Useful Relations page xiii xvii xviii xix Parti 1 Newtonian Particle Mechanics 1.1 Inertial Frames and the Galilean Transformation 1.2 Newton’s Laws of Motion 1.3 One-Dimensional Motion: Drag Forces 1.4 Oscillation in One-Dimensional Motion 1.5 Resonance 1.6 Motion in Two or Three Dimensions 1.7 Systems of Particles 1.8 Conservation Laws 1.9 Collisions 1.10 Forces of N ature 1.11 Summary Problems 2 Relativity 2.1 Einstein’s Postulates and the Lorentz Transformation 2.2 Relativistic Kinematics 2.3 Relativistic Dynamics 2.4 Summary Problems 3 The Variational Principle 3.1 3.2 3.3 3.4 3.5 3.6 VII Fermat’s Principle The Calculus of Variations Geodesics Brachistochrone Several Dependent Variables Mechanics from a Variational Principle З З 5 9 13 18 23 25 28 45 47 48 50 63 63 71 79 107 107 119 119 120 128 131 136 137
viii Contents 3.7 Motion in a Uniform Gravitational Field 3.8 Arbitrary Potential Energies 3.9 Summary Problems 139 145 146 147 4 Lagrangian Mechanics 4.1 Nonconservative Forces 4.2 Forces of Constraint and Generalized Coordinates 4.3 Hamilton’s Principle 4.4 Generalized Momenta and Cyclic Coordinates 4.5 Systems of Particles 4.6 The Hamiltonian 4.7 When is Η Ψ El 4.8 The Moral of Constraints 4.9 Small Oscillations about Equilibrium 4.10 Recap Problems 153 153 154 155 161 168 175 179 181 183 185 187 5 From Classical to Quantum and Back 5.1 Classical Waves 5.2 Two-Slit Experiments and Quantum Mechanics 5.3 Feynman Sum-over-Paths 5.4 Helium Atoms and the Two Slits, Revisited 5.5 The Emergence of the Classical Traj ectory 5.6 Why Hamilton’s Principle? 5.7 The Jacobi Action 5.8 Summary Problems 197 197 205 208 211 217 222 223 226 228 Partii 6 Constraints and Symmetries 6.1 Contact Forces 6.2 Symmetries and Conservation Laws: A Preview 6.3 Cyclic Coordinates and Generalized Momenta 6.4 A Less Straightforward Example 6.5 Infinitesimal Transformations 6.6 Symmetry 6.7 Noether’s Theorem 6.8 Some Comments on Symmetries 6.9 Summary Problems 233 233 245 246 248 250 253 255 266 267 267
Contents IX 7 Gravitation 7.1 Central Forces 7.2 The Two-Body Problem 7.3 The Effective Potential Energy 7.4 The Shape of Central-Force Orbits 7.5 Bertrand’s Theorem 7.6 Orbital Dynamics 7.7 The Viriai Theorem in Astrophysics 7.8 Summary Problems 8 Electromagnetism 8.1 Gravitation Revisited 8.2 The Lorentz Force Law 8.3 The Lagrangian for Electromagnetism 8.4 The Two-Body Problem, Once Again 8.5 Coulomb Scattering 8.6 Motion in a Uniform Magnetic Field 8.7 Relativistic Effects and the Electromagnetic Force 8.8 Summary Problems 9 Accelerating Frames 9.1 Linearly Accelerating Frames 9.2 Rotating Frames 9.3 Pseudoforces in Rotating Frames 9.4 Pseudoforces on Earth 9.5 Spacecraft Rendezvous and Docking 9.6 Summary Problems 10 From Black Holes to Random Forces 10.1 Beyond Newtonian Gravity 10.2 The Schwarzschild Geometry 10.3 Geodesics in the Schwarzschild Spacetime 10.4 The Event Horizon and Black Holes 10.5 Magnetic Gravity 10.6 Gauge Symmetry 10.7 Stochastic Forces 10.8 Summary Problems 275 275 277 280 284 292 293 302 304 305 314 314 318 323 326 328 332 348 351 351 358 358 362 365 370 378 386 386 395 395 400 405 413 415 418 421 427 427
x Contents Partiil 11 Hamiltonian Formulation 11.1 Legendre Transformations 11.2 Hamilton’s Equations 11.3 Phase Space 11.4 Canonical Transformations 11.5 Poisson Brackets 11.6 Poisson Brackets and Noether’s Theorem 11.7 Liouville’s Theorem 11.8 Summary Problems 437 438 442 445 451 457 462 465 466 467 12 Rigid-Body Dynamics 12.1 Rotation About a Fixed Axis 12.2 Euler’s Theorem 12.3 Rotation Matrices and the Body Frame 12.4 The Euler Angles 12.5 Infinitesimal Rotations 12.6 Angular Momentum 12.7 Principal Axes 12.8 Torque 12.9 Kinetic Energy 12.10 Potential Energy 12.11 Torque-Free Dynamics Using Euler Angles 12.12 Euler’s Equations of Motion and Stability 12.13 Gyroscopes 12.14 Summary Problems 474 474 476 478 482 485 489 496 502 503 506 511 516 519 522 523 13 Coupled Oscillators 13.1 Linear Systems of Masses and Springs 13.2 More Realistic Bound Systems 13.3 Vibrational Degrees of Freedom 13.4 The Continuum Limit 13.5 Summary Problems 530 530 542 550 552 567 567 14 Complex Systems 14.1 Integrability 14.2 Conservative Chaos 14.3 Dissipative Chaos 14.4 The Logistic Map 575 576 583 589 594
Contents XI 14.5 Perturbation Techniques 14.6 Numerical Techniques 14.7 Summary Problems 15 Seeds of Quantization 15.1 Hamilton-Jacobi Theory 15.2 Hamilton’s Characteristic Function 15.3 Action Angle Variables 15.4 Adiabatic Invariants 15.5 Early Quantum Theory 15.6 Optics: From Waves to Rays 15.7 Schrôdinger’s Wave Mechanics 15.8 Quantum Operators and the Bracket 15.9 A Hint at Quantum Time Evolution 15.10 Summary Problems 599 603 612 612 617 617 621 624 626 630 634 637 642 646 648 649 Appendices A Coordinate Systems 657 В Integral Theorems 663 C Dimensional Reasoning 670 D Fractal Dimension 674 E A Brief on Special Polynomials 676 F Taylor Series 678 Further Reading Index 680 682
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| adam_txt |
ям Contents Preface Acknowledgments and Credits Notation and Conventions Useful Relations page xiii xvii xviii xix Parti 1 Newtonian Particle Mechanics 1.1 Inertial Frames and the Galilean Transformation 1.2 Newton’s Laws of Motion 1.3 One-Dimensional Motion: Drag Forces 1.4 Oscillation in One-Dimensional Motion 1.5 Resonance 1.6 Motion in Two or Three Dimensions 1.7 Systems of Particles 1.8 Conservation Laws 1.9 Collisions 1.10 Forces of N ature 1.11 Summary Problems 2 Relativity 2.1 Einstein’s Postulates and the Lorentz Transformation 2.2 Relativistic Kinematics 2.3 Relativistic Dynamics 2.4 Summary Problems 3 The Variational Principle 3.1 3.2 3.3 3.4 3.5 3.6 VII Fermat’s Principle The Calculus of Variations Geodesics Brachistochrone Several Dependent Variables Mechanics from a Variational Principle З З 5 9 13 18 23 25 28 45 47 48 50 63 63 71 79 107 107 119 119 120 128 131 136 137
viii Contents 3.7 Motion in a Uniform Gravitational Field 3.8 Arbitrary Potential Energies 3.9 Summary Problems 139 145 146 147 4 Lagrangian Mechanics 4.1 Nonconservative Forces 4.2 Forces of Constraint and Generalized Coordinates 4.3 Hamilton’s Principle 4.4 Generalized Momenta and Cyclic Coordinates 4.5 Systems of Particles 4.6 The Hamiltonian 4.7 When is Η Ψ El 4.8 The Moral of Constraints 4.9 Small Oscillations about Equilibrium 4.10 Recap Problems 153 153 154 155 161 168 175 179 181 183 185 187 5 From Classical to Quantum and Back 5.1 Classical Waves 5.2 Two-Slit Experiments and Quantum Mechanics 5.3 Feynman Sum-over-Paths 5.4 Helium Atoms and the Two Slits, Revisited 5.5 The Emergence of the Classical Traj ectory 5.6 Why Hamilton’s Principle? 5.7 The Jacobi Action 5.8 Summary Problems 197 197 205 208 211 217 222 223 226 228 Partii 6 Constraints and Symmetries 6.1 Contact Forces 6.2 Symmetries and Conservation Laws: A Preview 6.3 Cyclic Coordinates and Generalized Momenta 6.4 A Less Straightforward Example 6.5 Infinitesimal Transformations 6.6 Symmetry 6.7 Noether’s Theorem 6.8 Some Comments on Symmetries 6.9 Summary Problems 233 233 245 246 248 250 253 255 266 267 267
Contents IX 7 Gravitation 7.1 Central Forces 7.2 The Two-Body Problem 7.3 The Effective Potential Energy 7.4 The Shape of Central-Force Orbits 7.5 Bertrand’s Theorem 7.6 Orbital Dynamics 7.7 The Viriai Theorem in Astrophysics 7.8 Summary Problems 8 Electromagnetism 8.1 Gravitation Revisited 8.2 The Lorentz Force Law 8.3 The Lagrangian for Electromagnetism 8.4 The Two-Body Problem, Once Again 8.5 Coulomb Scattering 8.6 Motion in a Uniform Magnetic Field 8.7 Relativistic Effects and the Electromagnetic Force 8.8 Summary Problems 9 Accelerating Frames 9.1 Linearly Accelerating Frames 9.2 Rotating Frames 9.3 Pseudoforces in Rotating Frames 9.4 Pseudoforces on Earth 9.5 Spacecraft Rendezvous and Docking 9.6 Summary Problems 10 From Black Holes to Random Forces 10.1 Beyond Newtonian Gravity 10.2 The Schwarzschild Geometry 10.3 Geodesics in the Schwarzschild Spacetime 10.4 The Event Horizon and Black Holes 10.5 Magnetic Gravity 10.6 Gauge Symmetry 10.7 Stochastic Forces 10.8 Summary Problems 275 275 277 280 284 292 293 302 304 305 314 314 318 323 326 328 332 348 351 351 358 358 362 365 370 378 386 386 395 395 400 405 413 415 418 421 427 427
x Contents Partiil 11 Hamiltonian Formulation 11.1 Legendre Transformations 11.2 Hamilton’s Equations 11.3 Phase Space 11.4 Canonical Transformations 11.5 Poisson Brackets 11.6 Poisson Brackets and Noether’s Theorem 11.7 Liouville’s Theorem 11.8 Summary Problems 437 438 442 445 451 457 462 465 466 467 12 Rigid-Body Dynamics 12.1 Rotation About a Fixed Axis 12.2 Euler’s Theorem 12.3 Rotation Matrices and the Body Frame 12.4 The Euler Angles 12.5 Infinitesimal Rotations 12.6 Angular Momentum 12.7 Principal Axes 12.8 Torque 12.9 Kinetic Energy 12.10 Potential Energy 12.11 Torque-Free Dynamics Using Euler Angles 12.12 Euler’s Equations of Motion and Stability 12.13 Gyroscopes 12.14 Summary Problems 474 474 476 478 482 485 489 496 502 503 506 511 516 519 522 523 13 Coupled Oscillators 13.1 Linear Systems of Masses and Springs 13.2 More Realistic Bound Systems 13.3 Vibrational Degrees of Freedom 13.4 The Continuum Limit 13.5 Summary Problems 530 530 542 550 552 567 567 14 Complex Systems 14.1 Integrability 14.2 Conservative Chaos 14.3 Dissipative Chaos 14.4 The Logistic Map 575 576 583 589 594
Contents XI 14.5 Perturbation Techniques 14.6 Numerical Techniques 14.7 Summary Problems 15 Seeds of Quantization 15.1 Hamilton-Jacobi Theory 15.2 Hamilton’s Characteristic Function 15.3 Action Angle Variables 15.4 Adiabatic Invariants 15.5 Early Quantum Theory 15.6 Optics: From Waves to Rays 15.7 Schrôdinger’s Wave Mechanics 15.8 Quantum Operators and the Bracket 15.9 A Hint at Quantum Time Evolution 15.10 Summary Problems 599 603 612 612 617 617 621 624 626 630 634 637 642 646 648 649 Appendices A Coordinate Systems 657 В Integral Theorems 663 C Dimensional Reasoning 670 D Fractal Dimension 674 E A Brief on Special Polynomials 676 F Taylor Series 678 Further Reading Index 680 682 |
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| isbn | 9781108834971 |
| language | English |
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| physical | xix, 687 Seiten Illustrationen, Diagramme |
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| spellingShingle | Helliwell, Thomas M. 1936- Modern classical mechanics Mechanik (DE-588)4038168-7 gnd |
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| title | Modern classical mechanics |
| title_auth | Modern classical mechanics |
| title_exact_search | Modern classical mechanics |
| title_exact_search_txtP | Modern classical mechanics |
| title_full | Modern classical mechanics T.M. Helliwell, Harvey Mudd College, California, V.V. Sahakian, Harvey Mudd College, California |
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| title_full_unstemmed | Modern classical mechanics T.M. Helliwell, Harvey Mudd College, California, V.V. Sahakian, Harvey Mudd College, California |
| title_short | Modern classical mechanics |
| title_sort | modern classical mechanics |
| topic | Mechanik (DE-588)4038168-7 gnd |
| topic_facet | Mechanik |
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Inhaltsverzeichnis
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