Book contents
- Frontmatter
- Contents
- Foreword by Sir William McCrea, FRS
- Preface to the fourth edition
- CHAPTER I KINEMATICAL PRELIMINARIES
- CHAPTER II THE EQUATIONS OF MOTION
- CHAPTER III PRINCIPLES AVAILABLE FOR THE INTEGRATION
- CHAPTER IV THE SOLUBLE PROBLEMS OF PARTICLE DYNAMICS
- CHAPTER V THE DYNAMICAL SPECIFICATION OF BODIES
- CHAPTER VI THE SOLUBLE PROBLEMS OF RIGID DYNAMICS
- CHAPTER VII THEORY OF VIBRATIONS
- CHAPTER VIII NON-HOLONOMIC SYSTEMS. DISSIPATIVE SYSTEMS
- CHAPTER IX THE PRINCIPLES OF LEAST ACTION AND LEAST CURVATURE
- CHAPTER X HAMILTONIAN SYSTEMS AND THEIR INTEGRAL-INVARIANTS
- CHAPTER XI THE TRANSFORMATION-THEORY OF DYNAMICS
- CHAPTER XII PROPERTIES OF THE INTEGRALS OF DYNAMICAL SYSTEMS
- CHAPTER XIII THE REDUCTION OF THE PROBLEM OF THREE BODIES
- CHAPTER XIV THE THEOREMS OF BRUNS AND POINCARÉ
- CHAPTER XV THE GENERAL THEORY OF ORBITS
- CHAPTER XVI INTEGRATION BY SERIES
- INDEX OF AUTHORS QUOTED
- INDEX OF TERMS EMPLOYED
CHAPTER II - THE EQUATIONS OF MOTION
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Foreword by Sir William McCrea, FRS
- Preface to the fourth edition
- CHAPTER I KINEMATICAL PRELIMINARIES
- CHAPTER II THE EQUATIONS OF MOTION
- CHAPTER III PRINCIPLES AVAILABLE FOR THE INTEGRATION
- CHAPTER IV THE SOLUBLE PROBLEMS OF PARTICLE DYNAMICS
- CHAPTER V THE DYNAMICAL SPECIFICATION OF BODIES
- CHAPTER VI THE SOLUBLE PROBLEMS OF RIGID DYNAMICS
- CHAPTER VII THEORY OF VIBRATIONS
- CHAPTER VIII NON-HOLONOMIC SYSTEMS. DISSIPATIVE SYSTEMS
- CHAPTER IX THE PRINCIPLES OF LEAST ACTION AND LEAST CURVATURE
- CHAPTER X HAMILTONIAN SYSTEMS AND THEIR INTEGRAL-INVARIANTS
- CHAPTER XI THE TRANSFORMATION-THEORY OF DYNAMICS
- CHAPTER XII PROPERTIES OF THE INTEGRALS OF DYNAMICAL SYSTEMS
- CHAPTER XIII THE REDUCTION OF THE PROBLEM OF THREE BODIES
- CHAPTER XIV THE THEOREMS OF BRUNS AND POINCARÉ
- CHAPTER XV THE GENERAL THEORY OF ORBITS
- CHAPTER XVI INTEGRATION BY SERIES
- INDEX OF AUTHORS QUOTED
- INDEX OF TERMS EMPLOYED
Summary
The ideas of rest and motion.
In the previous chapter we have frequently used the terms “fixed” and “moving” as applied to systems. So long as we are occupied with purely kinematical considerations, it is unnecessary to enter into the ultimate significance of these words; all that is meant is, that we consider the displacement of the “moving” systems, so far as it affects their configuration with respect to the systems which are called “fixed,” leaving on one side the question of what is meant by absolute “fixity.”
When however we come to consider the motion of bodies as due to specific causes, this question can no longer be disregarded.
In popular language the word “fixed” is generally used of terrestrial objects to denote invariable position relative to the surface of the earth at the place considered. But the earth is rotating on its axis, and at the same time revolving round the Sun, while the Sun in turn, accompanied by all the planets, is moving with a large velocity along some not very accurately known direction in space. It seems hopeless therefore to attempt to find anything which can be really considered to be “at rest.”
In the nineteenth century it was supposed that the aether of space (the vehicle of light and of electric and magnetic actions) was (apart from small vibratory motions) stagnant, and so was capable of providing a basis for absolute fixity.
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- Publisher: Cambridge University PressPrint publication year: 1988