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This book deals with theoretical mechanics. Newton published the "Philosophiæ Naturalis Principia Mathematica" in 1687. In it, he sets out the basic principles of physics that are required to understand the motion of the planets, their moons, and the comets in the solar system. It includes the gravitational (inverse square) law, the inertial principle, and the basic elements of mechanics. Since its publication, a large number of refinements and reformulations have been introduced, thereby adding enormous insight into the structure of mechanics, which is commonly known as "classical mechanics". All these have in common that by taking a suitable limit, Newton's original principles re-appear. Thus, physicists and mathematicians who work on the subject always have a notion that if their theories do not return to Newton's foundations, then there is something wrong. Newton himself acknowledged that 'if I have seen further (than others), it is by standing on the shoulders of giants'. One of these giants was undoubtedly Galileo who died in the year Newton was born. So, Newton himself adhered to the 'classical limit'.
Professor Koenders (FIMA, CMath), MInstP, CPhys, (CSci) has a background in theoretical physics, notably in statistical mechanics. He has expertise in the theory of fluctuations in continuum mechanics, and much of his work has been concerned with developing the micromechanical basis for the behaviour of dense granular media including elastic-frictional densely packed material and slurry flows. Assisted by funding from the Dutch Government, the US Air Force, industry in the UK and overseas, as well as EPSRC, he has been able to apply the theoretical techniques to erosion flows in geotechnical filters, the characteristics of densely packed media, the cake formation process in filtration, and a number of contributions to geophysical flows. His cross-disciplinary interests are enhanced by numerous collaborations both in the UK, the USA, and in Europe. He has contributed some 100 scientific publications on topics in mechanics.
1. Newtonian Mechanics.- 2. Newtonian Mechanics Reformulated.- 3. Two Body Problem and the Solar System.- 4. Special Relativity Theory.- 5. The Newtonian Gravitational Interaction.- 6. Mechanics using Integral Principles.- 7. Many-Particle Systems.- 8. Elements of Quantum Mechanics.
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