vol 4: Glossary
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Newtonian mechanics
[Borowski, mechanics]
Newtonian mechanics develops the mathematical and physical consequences of Newton's three laws of motion:
Law 1: Every body continues in its state of rest or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.
Law 2: The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
Law 3: Top every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
Law of Universal Gravitation: The gravitation force exerted by two bodies upon one another is proportional to the product of their masses divided by the square of the distance between them.
Of these laws, the second is the most fruitful, since it allows us to model mathematically the relationships of force, mass, acceleration, position and velocity through the very simple formula F = ma. This law can be expressed as a differential equation. Here in one dimension:
where F = force, m = mass, x = position and t = time and a = acceleration.
The solution of this equation for different laws of force, subject to various boundary conditions, forms the heart of Newtonian mechanics. Although these laws look very simple, and can readily be applied to two bodies, it was soon found that their application to three or more bodies was fraught with difficulty, and could only be achieved using approximations.
This and other problems arising from Newtonain mechanics led to an explosion in mathematics over the new few centuries.
Further reading
Books
| Feynman, Richard P et al, The Feynman Lectures on Physics (volume 1) : Mainly Mechanics, Radiation and Heat, Addison Wesley 1963 Amazon back |
| Mach, Ernst , The Science of Mechanics (translated by Thomas J McCormack), Open Court 1988 Amazon back |
| Misner, Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. ... this is a book on Einstein's theory of gravity (general relativity).' Amazon back |
| Moulton, Forest Ray, An Introduction to Celestial Mechanics, Dover 1970 Jacket: 'An unrivalled text in the field of celestial mechanics, Moulton's theoretical work on the prediction and interpretation of celestial phenomena has not been superseded.' Amazon back |
| Newton, Isaac, Philosophiae Naturalis Principia Mathematica , Harvard University Press 1972 One of the most important contributions to human knowledge. First translated from the Latin by Andrew Motte in 1729, Amazon back |
| Newton, Isaac, and Julia Budenz, I. Benard Cohen, Anne Whitman (Translators) , The Principia : Mathematical Principles of Natural Philosophy , University of California Press 1999 This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. ... The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students. Amazon back |
Links
| Mathematical Archives Calculus Resources on Line 'Welcome to the Calculus Resources On-line area of the Mathematics Archives. This area contains information and links to numerous Internet resources, which could be used for teaching and learning of calculus.' back |
| Newton.org Sir Isaac Newton 'Welcome to newton.org.uk - the virtual museum of Sir Isaac Newton and the history of science.' back |
| Cambridge University Isaac Newton Links 'Here at the Isaac Newton Institute for Mathematical Sciences, we are often asked about Newton's life and works. There are already many excellent and informative Web sites and books about Newton, so rather than duplicate those, we have put together a guide to some of the places, both real and virtual, where you can find out more.' back |
| Imperial College The Newton Project 'The magnitude of Isaac Newton's (1642-1727) accomplishments place him in the very first rank of scientists and mathematicians. However, although most early modern scientists have been honoured with comprehensive editions of their collected works, there is no similar tribute to Newton. There are excellent editions of his mathematical and scientific papers, but very few of his non-scientific writings have appeared in print. Accordingly, the Newton Project, based at Cambridge University and Imperial College, was formed in 1998 to produce both electronic and printed editions of Newton's theological, alchemical and Mint papers. These editions will shed light on the differences and connections between distinct areas of his research. For example, there are a number of links between different elements in Newton's work, such as theology and natural philosophy, and he himself thought that his scientific discoveries constituted evidence for the existence of an Omnipotent and mathematically adept Creator.' back |
| University of Tennessee Newton's Three Laws of Motion Astronomy 161: The Solar System, Department of Physics and Astronomy, University of Tennessee. back |
| University of Tennessee Sir Isaac Newton: The Universal Law of Grtavitation Astronomy 161: The Solar System, Department of Physics and Astronomy, University of Tennessee. back |
| University of Tennessee Sir Isaac Newton and the Unification of Physics and Astronomy. Astronomy 161: The Solar System, Department of Physics and Astronomy, University of Tennessee. back |
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