Book contents
- Frontmatter
- Contents
- Preface
- Chapter 1 INTRODUCTION TO THE MECHANICAL UNIVERSE (Program 1)
- Chapter 2 THE LAW OF FALLING BODIES (Program 2)
- Chapter 3 THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS
- Chapter 4 INERTIA
- Chapter 5 VECTORS
- Chapter 6 NEWTON'S LAWS AND EQUILIBRIUM
- Chapter 7 UNIVERSAL GRAVITATION AND CIRCULAR MOTION
- Chapter 8 FORCES
- Chapter 9 FORCES IN ACCELERATING REFERENCE FRAMES
- Chapter 10 ENERGY: CONSERVATION AND CONVERSION
- Chapter 11 THE CONSERVATION OF MOMENTUM
- Chapter 12 OSCILLATORY MOTION
- Chapter 13 ANGULAR MOMENTUM
- Chapter 14 ROTATIONAL DYNAMICS FOR RIGID BODIES
- Chapter 15 GYROSCOPES
- Chapter 16 KEPLER'S LAWS AND THE CONIC SECTIONS
- Chapter 17 SOLVING THE KEPLER PROBLEM
- Chapter 18 NAVIGATING IN SPACE
- Chapter 19 TEMPERATURE AND THE GAS LAWS
- Chapter 20 THE ENGINE OF NATURE
- Chapter 21 ENTROPY
- Chapter 22 THE QUEST FOR LOW TEMPERATURE
- Appendix A THE INTERNATIONAL SYSTEM OF UNITS
- Appendix B CONVERSION FACTORS
- Appendix C FORMULAS FROM ALGEBRA, GEOMETRY, AND TRIGONOMETRY
- Appendix D ASTRONOMICAL DATA
- Appendix E PHYSICAL CONSTANTS
- SELECTED BIBLIOGRAPHY
- Index
Chapter 5 - VECTORS
Published online by Cambridge University Press: 05 August 2013
- Frontmatter
- Contents
- Preface
- Chapter 1 INTRODUCTION TO THE MECHANICAL UNIVERSE (Program 1)
- Chapter 2 THE LAW OF FALLING BODIES (Program 2)
- Chapter 3 THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS
- Chapter 4 INERTIA
- Chapter 5 VECTORS
- Chapter 6 NEWTON'S LAWS AND EQUILIBRIUM
- Chapter 7 UNIVERSAL GRAVITATION AND CIRCULAR MOTION
- Chapter 8 FORCES
- Chapter 9 FORCES IN ACCELERATING REFERENCE FRAMES
- Chapter 10 ENERGY: CONSERVATION AND CONVERSION
- Chapter 11 THE CONSERVATION OF MOMENTUM
- Chapter 12 OSCILLATORY MOTION
- Chapter 13 ANGULAR MOMENTUM
- Chapter 14 ROTATIONAL DYNAMICS FOR RIGID BODIES
- Chapter 15 GYROSCOPES
- Chapter 16 KEPLER'S LAWS AND THE CONIC SECTIONS
- Chapter 17 SOLVING THE KEPLER PROBLEM
- Chapter 18 NAVIGATING IN SPACE
- Chapter 19 TEMPERATURE AND THE GAS LAWS
- Chapter 20 THE ENGINE OF NATURE
- Chapter 21 ENTROPY
- Chapter 22 THE QUEST FOR LOW TEMPERATURE
- Appendix A THE INTERNATIONAL SYSTEM OF UNITS
- Appendix B CONVERSION FACTORS
- Appendix C FORMULAS FROM ALGEBRA, GEOMETRY, AND TRIGONOMETRY
- Appendix D ASTRONOMICAL DATA
- Appendix E PHYSICAL CONSTANTS
- SELECTED BIBLIOGRAPHY
- Index
Summary
If I wished to attract the student of any of these sciences to an algebra for vectors, I should tell him that the fundamental notions of this algebra were exactly those with which he was daily conversant. … In fact, I should tell him that the notions which we use in vector analysis are those which he who reads between the lines will meet on every page of the great masters of analysis, or of those who have probed the deepest secrets of nature. …
J. W. Gibbs (in Nature, 16 March 1893)COORDINATE SYSTEMS
Galileo discovered through the law of inertia that there is no single preferred reference frame. To use this discovery most efficiently, we need to discuss some geometrical ideas. The first kind of geometrical construction we need is a way of describing where things are.
If the world were only one-dimensional, everything would be on a single line. To describe where something is on that line we would first pick a point on the line as a point of reference, the origin. Then we would pick a direction along the line as the positive direction – let's say to the right of the starting point. And having made those choices we would only need to give one number – call it the x coordinate – to specify the location of a point.
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- Information
- The Mechanical UniverseMechanics and Heat, Advanced Edition, pp. 75 - 112Publisher: Cambridge University PressPrint publication year: 1986