Mechanics

Devoted to the foundation of mechanics, namely classical Newtonian mechanics, the subject is based mainly on Galileo's principle of relativity and Hamilton's principle of least action. The exposition is simple and leads to the most complete direct means of solving problems in mechanics. The final sections on adiabatic invariants have been revised and augmented. In addition a short biography of L D Landau has been inserted.

Preface to the third English edition

vii

L. D. Landau---a biography

ix

I. THE EQUATIONS OF MOTION

Generalised co-ordinates

1

(1)

The principle of least action

2

(2)

Galileo's relativity principle

4

(2)

The Lagrangian for a free particle

6

(2)

The Lagrangian for a system of particles

8

(5)

II. CONSERVATION LAWS

Energy

13

(2)

Momentum

15

(1)

Centre of mass

16

(2)

Angular momentum

18

(4)

Mechanical similarity

22

(3)

III. INTEGRATION OF THE EQUATIONS OF MOTION

Motion in one dimension

25

(2)

Determination of the potential energy from the period of oscillation

27

(2)

The reduced mass

29

(1)

Motion in a central field

30

(5)

Kepler's problem

35

(6)

IV COLLISIONS BETWEEN PARTICLES

Disintegration of particles

41

(3)

Elastic collisions

44

(4)

Scattering

48

(5)

Rutherford's formula

53

(2)

Small-angle scattering

55

(3)

V. SMALL OSCILLATIONS

Free oscillations in one dimension

58

(3)

Forced oscillations

61

(4)

Oscillations of systems with more than one degree of freedom

65

(5)

Vibrations of molecules

70

(4)

Damped oscillations

74

(3)

Forced oscillations under friction

77

(3)

Parametric resonance

80

(4)

Anharmonic oscillations

84

(3)

Resonance in non-linear oscillations

87

(6)

Motion in a rapidly oscillating field

93

(3)

VI MOTION OF A RIGID BODY

Angular velocity

96

(2)

The inertia tensor

98

(7)

Angular momentum of a rigid body

105

(2)

The equations of motion of a rigid body

107

(3)

Eulerian angles

110

(4)

Euler's equations

114

(2)

The asymmetrical top

116

(6)

Rigid bodies in contact

122

(4)

Motion in a non-inertial frame of reference

126

(5)

VII. THE CANONICAL EQUATIONS

Hamilton's equations

131

(2)

The Routhian

133

(2)

Poisson brackets

135

(3)

The action as a function of the co-ordinates

138

(2)

Maupertuis' principle

140

(3)

Canonical transformations

143

(3)

Liouville's theorem

146

(1)

The Hamilton-Jacobi equation

147

(2)

Separation of the variables

149

(5)

Adiabatic invariants

154

(3)

Canonical variables

157

(2)

Accuracy of conservation of the adiabatic invariant

159

(3)

Conditionally periodic motion

162

(5)

Index

167

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