# Book:D.E. Rutherford/Classical Mechanics/Third Edition

## D.E. Rutherford: Classical Mechanics (3rd Edition)

Published $\text {1964}$, Oliver and Boyd.

### Contents

Preface
Preface to the Third Edition
Introduction

chapter $\text {I}$ Kinematics
1. Space and time
2. Velocity and acceleration
3. Relative velocity
4. Angular velocity
5. Coplanar moving area
6. Rate of change of a vector moving relative to moving axes
7. Kinematics of a rigid body
8. Instantaneous axis of rotation
Examples $\text {I}$

chapter $\text {II}$ The Nature of Force
9. Newton's laws of motion
10. Further consideration of Newton's laws
11. Polygon of forces
12. Kepler's laws
13. Newton's law of gravitation
14. Attraction due to a uniform circular ring at a point on its axis
15. Attraction due to a uniform spherical shell
16. Attraction due to a distribution of matter with spherical symmetry
17. Weight
18. Electromagnetic forces
19. Elastic forces
20. Central forces
21. Centrifugal forces
22. Conservative forces
23. Potential energy
24. Conservation of energy
25. Constrained movement of a particle
26. The rough inclined plane
Examples $\text {II}$

chapter $\text {III}$ Dynamics of a Particle
27. Rectilinear motion
28. Rectilinear motion under a constant force
29. Rectilinear motion under a resistance proportional to the velocity
30. Falling raindrop
31. Simple harmonic motion
32. Damped oscillator with a periodic applied force
33. The equation $\ddot x = n^2 x$
34. Probabilities
35. Coplanar motion
36. Projectiles
37. Projectile in a resisting medium
38. Orbit of a particle under a central force
39. Orbit of a particle under an inverse square attractive force
40. Planetary motion
41. Moons
42. Kepler's equation of time
43. Orbit of a particle under an inverse square repulsive force
44. Determination of a central force from the orbit
45. The simple pendulum and allied problems
46. Charged particles in a magnetic field
47. Momentum
48. Recoil of a gun
49. Rectilinear motion of a rocket
50. Moment of a localised vector
51. Moment of momentum
52. Impulsive forces
53. Collisions
54. An example of constrained motion
55. Motion relative to the earth
Examples $\text {III}$

chapter $\text {IV}$ Dynamics of Rigid Bodies
56. The mass centre
57. The motion of the mass centre
58. Moment of momentum of a system of particles
59. Kinetic energy of a system of particles
60. Rigid bodies
61. Impulsive motion of a rigid body
62. Potential energy
63. Equivalent systems of forces
64. Poinsot's central axis
65. Centre of gravity
66. Equilibrium
67. Virtual work
68. Equations of motion
69. Kinetic energy in two-dimensional problems
70. An example on impulsive motion
71. Small oscillations
72. Compound pendulum
73. Stability of equilibrium
74. Moments and products of inertia
75. Evaluation of the moments and products of inertia
76. Rotation of the axes
77. Translation of the axes
78. The kinetic energy of a rigid body
79. Euler's equations of motion
80. Eulerian nutation
81. Steady precession of a gyrostat
82. The Eulerian angles
83. Motion of the spinning top
84. Steady precession of a top
Examples $\text {IV}$

chapter $\text {V}$ Generalised Coordinates
85. Holonomic systems
86. Lagrange's equations for a holonomic system
87. Lagrange's equations for impulsive forces
88. The Lagrangian function
89. Ignorable coordinates
90. Theory of small vibrations
91. Normal modes
92. Normal coordinates
93. Particles on a taut string
94. Conditions for stable equilibrium
95. Hamilton's equations
96. Hamilton's principle
97. Hamilton's principal function
Examples $\text {V}$
Index

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