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Ⅰ．THE EQUATIONS OF MOTION 1

1．Generalised co-ordinates 1

2．The principle of least action 2

3．Galileo's relativity principle 4

4．The Lagrangian for a free particle 6

5．The Lagrangian for a system of particles 8

Ⅱ．CONSERVATION LAWS 13

6．Energy 13

7．Momentum 15

8．Centre of mass 16

9．Angular momentum 18

0．Mechanical similarity 22

Ⅲ．INTEGRATION OF THE EQUATIONS OF MOTION 22

11．Motion in one dimension 25

12．Determination of the potential energy from the period of oscillation 27

13．The reduced mass 29

14．Motion in a central field 30

15．Kepler's problem 35

Ⅳ．COLLISIONS BETWEEN PARTICLES 41

16．Disintegration of particles 41

17．Elastic collisions 44

18．Scattering 48

19．Rutherford's formula 53

20．Small-angle scattering 55

Ⅴ．SMALL OSCILLATIONS 58

21．Free oscillations in one dimension 58

22．Foreed oscillations 61

23．Oscillations of systems with more than one degree offreedom 65

24．Vibrations of molecules 70

25．Damped oscillations 74

26．Forced oscillations under friction 77

27．Parametric resonance 80

28．Anharmonic oscillations 84

29．Resonance in non-linear oscillations 87

30．Motionin arapidly oscillatingfield 93

Ⅵ．MOTION OF A RIGID BODY 96

31．Angular velocity 96

32．The inertia tensor 98

33．Angular momentum of a rigid body 105

34．The equations of motion of a rigid body 107

35．Eulerian angles 110

36．Euler's equations 114

37．The asymmctrical top 116

38．Rigidbodies in contact 122

39．Motion in a non-inertial frame of reference 126

Ⅶ．THE CANONICAL EQUATIONS 131

40．Hamilton's equations 131

41．The Routhian 133

42．Poisson brackets 135

43．The action as a function ofthe co-ordinates 138

44．Maupertuis' principle 140

45．Canonical transformations 143

46．Liouville's theorem 146

47．The Hamilton-Jacobi equation 147

48．Separation of thevariables 149

49．Adiabatic invariants 154

50．Canonical variables 157

51．Accuracy of conservation of the adiabatic invariant 159

52．Conditionally periodic motion 162

Index 167