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1 | (18) |
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2 | (3) |
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1.1.1 Generalized Coordinates |
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2 | (1) |
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2 | (1) |
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2 | (1) |
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3 | (1) |
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3 | (1) |
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1.1.6 Lagrange Equations for Systems with Constraints |
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4 | (1) |
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1.1.7 Lagrange Equations with Impulse Forces |
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4 | (1) |
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5 | (14) |
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1.2.1 Exercise 1: Double Pendulum |
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5 | (2) |
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1.2.2 Exercise 2: Particle on a Paraboloid |
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7 | (2) |
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1.2.3 Exercise 3: Sphere Rolling on Another Sphere |
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9 | (3) |
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1.2.4 Exercise 4: Truck Descending a Slope |
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12 | (4) |
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1.2.5 Exercise 5: Sliding and Rotating Masses |
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16 | (3) |
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19 | (6) |
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20 | (1) |
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20 | (1) |
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20 | (1) |
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2.1.3 Conservative System |
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20 | (1) |
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2.1.4 Expression of the Hamiltonian in Different Coordinate Systems |
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21 | (1) |
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21 | (4) |
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2.2.1 Exercise 6: Particle in a Plane with Central Force |
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21 | (2) |
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2.2.2 Exercise 7: Harmonic Oscillator |
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23 | (2) |
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3 First Integral and Variational Principle |
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25 | (14) |
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25 | (3) |
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25 | (1) |
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25 | (1) |
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26 | (1) |
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27 | (1) |
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3.1.5 Variational Principle |
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27 | (1) |
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3.1.6 Application in Optics: Fermat Principle |
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27 | (1) |
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28 | (11) |
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3.2.1 Exercise 8: Watt Regulator |
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28 | (1) |
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3.2.2 Exercise 9: First Integral of a Free Material Point |
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29 | (1) |
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3.2.3 Exercise 10: Brachistochrone Problem |
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30 | (3) |
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3.2.4 Exercise 11: Minimum Surface of Revolution |
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33 | (2) |
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3.2.5 Exercise 12: Optical Path and Fermat Principle |
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35 | (4) |
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4 Canonical Transformations or Contact Transformations |
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39 | (12) |
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39 | (2) |
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4.1.1 Canonical Transformations |
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39 | (1) |
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4.1.2 Condition for a Transformation to be Canonical |
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40 | (1) |
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4.1.3 Generating Functions |
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40 | (1) |
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41 | (10) |
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4.2.1 Exercise 13: Canonical Transformation 1 |
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41 | (3) |
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4.2.2 Exercise 14: Canonical Transformation 2 |
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44 | (1) |
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4.2.3 Exercise 15: Canonical Transformation 3 |
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44 | (1) |
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4.2.4 Exercise 16: Canonical Transformation 4 |
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45 | (1) |
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4.2.5 Exercise 17: Canonical Transformation 5 |
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45 | (1) |
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4.2.6 Exercise 18: Canonical Transformation 6 |
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46 | (1) |
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4.2.7 Exercise 19: Canonical Transformation 7 |
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47 | (1) |
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4.2.8 Exercise 20: Canonical Transformation 8 and Harmonic Oscillator 2 |
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48 | (3) |
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5 Hamilton--Jacobi Equations |
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51 | (40) |
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51 | (2) |
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5.1.1 Hamilton--Jacobi Equations |
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51 | (1) |
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5.1.2 Solution of Hamilton--Jacobi Equations |
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52 | (1) |
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5.1.3 Time Independent Hamiltonian |
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52 | (1) |
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53 | (38) |
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5.2.1 Exercise 21: Harmonic Oscillator 3 |
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53 | (2) |
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5.2.2 Exercise 22: Free Falling Particle |
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55 | (2) |
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5.2.3 Exercise 23: Ballistic Flight of a Projectile |
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57 | (3) |
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5.2.4 Exercise 24: Particle Sliding on an Inclined Plane |
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60 | (2) |
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5.2.5 Exercise 25: Connected Particles Sliding on Inclined Surfaces |
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62 | (2) |
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5.2.6 Exercise 26: Unconventional Mechanics |
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64 | (2) |
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5.2.7 Exercise 27: Double Pendulum 2 |
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66 | (2) |
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5.2.8 Exercise 28: Classical Problem of Kepler |
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68 | (5) |
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5.2.9 Additional Note on the Classical Problem of Kepler |
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73 | (1) |
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5.2.10 Exercise 29: Particle and Potential in --- Kcosθ/r2 |
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74 | (3) |
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5.2.11 Exercise 30: Schrodinger Equation |
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77 | (2) |
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5.2.12 Exercise 31: Stark Effect |
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79 | (7) |
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5.2.13 Exercise 32: Particle in a Double Coulomb Field |
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86 | (3) |
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5.2.14 Exercise 33: Particle in Coulomb and Uniform Fields |
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89 | (2) |
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6 Phase Integral and Action-Angle Variables |
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91 | (34) |
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91 | (1) |
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91 | (1) |
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6.1.2 Frequency and Angular Variable |
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92 | (1) |
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92 | (33) |
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6.2.1 Exercise 34: Harmonic Oscillator 4 |
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92 | (1) |
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6.2.2 Exercise 35: Small Oscillations of the Pendulum |
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93 | (8) |
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6.2.3 Exercise 36: Three Dimension Harmonic Oscillator |
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101 | (4) |
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6.2.4 Exercise 37: Energy in a Bohr Atom |
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105 | (4) |
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6.2.5 Exercise 38: Classical Kepler Problem 2 |
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109 | (5) |
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6.2.6 Exercise 39: Relativistic Kepler Problem |
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114 | (4) |
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6.2.7 Exercise 40: Advance of Mercury Perihelion |
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118 | (7) |
Selected Bibliography |
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125 | (2) |
Index |
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127 | |