Dynamics

Cover......Page 1
Frontmatter......Page 6
PREFACE......Page 10
Contents......Page 12
ART. 1. Velocity......Page 18
ART. 2. Acceleration......Page 20
ART. 3. Units and Dimensions......Page 23
ART. 4. The Acceleration of Gravity......Page 25
ART. 6. Differential Equations......Page 26
Examples I......Page 31
ART. 6. Dynamical Principles. Gravitational Units......Page 34
ART. 7. The Absolute System of Dynamics......Page 37
ART. 8. Application to Gravity......Page 38
ART. 9. General Equation of Motion. Impulse......Page 40
ART. 10. Simple-Harmonic Motion......Page 41
ART. 11. The Pendulum......Page 46
ART. 12. Disturbed Simple-Harmonic Motion. Constant Disturbing Force......Page 47
ART. 13. Periodic Disturbing Force......Page 49
ART. 14. General Disturbing Force......Page 53
ART. 15. Motion about Unstable Equilibrium......Page 55
ART. 16. Motion under Variable Gravity......Page 56
ART. 17. Work; Power......Page 58
ART. 18. Equation of Energy......Page 60
ART. 19. Dynamical Units and their Dimensions......Page 63
Examples II, III, IV......Page 66
ART. 20. Velocity......Page 72
ART. 21. Hodograph. Acceleration......Page 75
ART. 22. Relative Motion......Page 78
ART. 23. Epicyclic Motion......Page 79
ART. 24. Superposition of Simple-Harmonic Vibrations......Page 81
Examples V.......Page 83
ART. 25. Dynamical Principle......Page 86
ART. 26. Cartesian Equations......Page 88
ART. 27. Motion of a Projectile......Page 89
ART. 28. Elliptic-Harmonic Motion......Page 93
ART. 29. Spherical Pendulum. Blackburn's Pendulum......Page 96
ART. 30. Equation of Energy......Page 98
ART. 31. Properties of a Conservative Field of Force......Page 101
ART. 32. Oscillations about Equilibrium. Stability......Page 102
ART. 33. Rotating Axes......Page 105
Examples VI, VII, VIII......Page 109
ART. 34. Tangential and Normal Accelerations......Page 115
ART. 35. Dynamical Equations......Page 118
ART. 36. Motion on a Smooth Curve......Page 120
ART. 37. The Circular Pendulum......Page 122
ART. 38. The Cycloidal Pendulum......Page 127
ART. 39. Oscillations on a Smooth Curve; Finite Amplitude......Page 130
Examples IX. X......Page 133
ART. 40. Conservation of Momentum......Page 138
ART. 41. Instantaneous Impulses. Impact......Page 140
ART. 42. Kinetic Energy......Page 143
ART. 43. Conservation of Energy......Page 144
ART. 44. Oscillations about Equilibrium......Page 146
Examples XI......Page 151
ART. 45. Linear and Angular Momentum......Page 154
ART. 46. Kinetic Energy......Page 156
ART. 48. Principle of Angular Momentum......Page 158
ART. 49. Motion of a Chain......Page 159
ART. 50. Steady Motion of a Chain......Page 161
ART. 51. Impulsive Motion of a Chain......Page 164
Examples XII......Page 165
ART. 53. D'Alembert's Principle......Page 167
ART. 54. Rotation about a Fixed Axis......Page 172
ART. 55. The Compound Pendulum......Page 175
ART. 56. Determination of g......Page 177
ART. 57. Torsional Oscillations......Page 180
ART. 58. Bifilar Suspension......Page 181
ART. 59. Reactions on a Fixed Axis......Page 182
ART. 60. Application to the Pendulum......Page 184
Examples XIII, XIV......Page 186
ART. 61. Comparison of Angular Momenta about Parallel Axes......Page 190
ART. 62. Kate of Change of Angular Momentum......Page 192
ART. 63. Application to Rigid Bodies......Page 194
ART. 64. Equation of Energy......Page 198
ART. 65. General Theory of a System with One Degree of Freedom......Page 200
ART. 66. Oscillations about Equilibrium. Stability......Page 203
ART. 67. Forced Oscillations of a Pendulum. Seismographs......Page 209
ART. 68. Oscillations of Multiple Systems......Page 213
ART. 69. Stresses in a Moving Body......Page 215
ART. 70. Initial Reactions......Page 217
ART. 71. Instantaneous Impulses......Page 219
ART. 72. The Ballistic Pendulum......Page 224
ART. 73. Effect of Impulses on Energy......Page 226
Examples XV, XVI......Page 227
ART. 74 Statement of the Law......Page 233
ART. 75. Simple Astronomical Applications......Page 234
ART. 76. The Problem of Two Bodiea......Page 236
ART. 77. Construction of Orbits......Page 240
ART. 78. Hodograph......Page 244
ART. 79. Formulas for Elliptic Motion......Page 245
ART. 80. Kepler's Three Laws......Page 248
ART. 81. Correction to Kepler's Third Law......Page 251
ART. 82. Perturbations......Page 254
ART. 83. The Constant of Gravitation......Page 258
Examples XVII, XVIII, XIX......Page 260
ART. 84. Determination of the Orbit......Page 264
ART. 85. The Inverse Problem......Page 266
ART. 86. Polar Coordinates......Page 268
ART. 87. Disturbed Circular Orbit......Page 273
ART. 88 Apses......Page 276
ART. 89. Critical Orbits......Page 278
ART. 90. Differential Equation of Central Orbits......Page 280
ART. 91. Law of the Inverse Cube......Page 283
Examples XX......Page 288
ART. 92. Resistance varying as the Velocity......Page 291
ART. 93. Constant Propelling Force, with Resistance......Page 293
ART. 94. Theory of Damped Oscillations......Page 294
ART. 95. Forced Oscillations......Page 299
ART. 96. The Spherical Pendulum......Page 304
ART. 97. Quadratic Law of Resistance......Page 307
ART. 98. Case of a Constant Propelling Force......Page 308
ART. 99. Effect of Resistance on Projectiles......Page 311
ART. 100. Effect of Resistance on Planetary Orbits......Page 314
Examples XXI......Page 315
ART. 101. Motion of a Particle on a Smooth Surface......Page 318
ART. 102. Motion on a Spherical Surface......Page 320
ART. 103. The Spherical Pendulum......Page 322
ART. 104. General Motion of a Particle. Lagrange's Equations......Page 325
ART. 105. Applications......Page 330
ART. 106. Mechanical Systems of Double Freedom. Lagrange's Equations......Page 333
ART. 107. Energy. Momentum. Impulse......Page 337
ART. 108. General Theorems......Page 339
ART. 109. Oscillations about Equilibrium......Page 341
ART. 110. Normal Modes of Vibration......Page 345
ART. 111. Forced Oscillations......Page 348
Examples XXII, XXIII......Page 351
APPENDIX. NOTE ON DYNAMICAL PRINCIPLES......Page 362
INDEX......Page 367