- How does quantum mechanics differ from classical mechanics?
- Classical Mechanics — SymPy documentation
- Classical Mechanics, Philosophy of
What I find remarkable about the book of de Lange and Pierrus, is that the authors, who are academics at the University of KwaZulu-Natal, even dared to embark on this hefty project about pages , in a field that is clearly mature and very well established. Did they have the foresight to carve out a niche that makes their contribution unique and useful in a very crowded subject area? The answer is yes and emphatically so. The authors make significant contributions to classical mechanics by considering more complex - and hence more realistic - problems, many of which are only tractable on the computer.
How does quantum mechanics differ from classical mechanics?
They use Mathematica, which is a useful symbolic manipulation package, to solve their problems. They give excerpts of their computer code, which is very readable. By presenting their computational methodology in such detail, the authors are helping the reader to understand the algorithmic structures of their solutions which are readily transferable to other programming languages. In these respects, the book is enormously pedagogical and useful. It is a very good resource for teaching standard theoretical and computational classical mechanics.
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Considering that classical mechanics is basic to both physics and practically all the engineering disciplines, there is potentially a very wide readership. The range of topics within the book is very impressive.
The authors cover problems in one, two and three dimensions, as well as problems involving linear oscillations, energy and potentials, momentum and angular momentum, multiparticle systems, rigid bodies, non-linear oscillations, reference frames and the relativity principle. The book is written in the form of problems with solutions and with comments. The solutions are often accompanied by graphical representations. Students would do well to turn some of these solutions to graphical animations using visualisation tools.
The authors could perhaps continue to be involved in this project by making their visualisation resources available on the web. Their comments are very insightful and often point to something new that can and should be explored further by the reader.
Classical Mechanics — SymPy documentation
This exploration in turn encourages the reader to build on the programming solutions provided by the authors. I found the final chapter, 'The relativity principle and some of its consequences', to be especially elucidating, and the problems very instructive and even suggestive. If one asserts that the laws of physics are equally valid in all inertial frames, then the notion of a universal speed emerges very naturally, and the mystery that is often accompanied by Einstein's theory of special relativity dissipates quite quickly. Although it is the oldest branch of physics, the term "classical mechanics" is relatively new.
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Soon after , a series of revolutions in mathematical thinking gave birth to new fields of inquiry: relativistic mechanics for phenomena relating to the very fast, and quantum mechanics for phenomena relating to the very small. The equations developed prior to were still perfectly suitable for describing objects of everyday sizes and speeds.
However, because this older branch of physics existed alongside two new ones, it needed a new name. The term "classical mechanics" was coined to loosely label the set of equations that describe reality at scales where quantum and relativistic effects are negligible. This work unified mathematical reasoning with relatively new ideas about motion here on the Earth's surface, and the most ancient of all fields of scientific inquiry: astronomy.
The ancient civilizations of Mesopotamia, Egypt and the Indus Valley all demonstrated an understanding of the motion of the sun, moon and stars; they could even predict the dates of eclipses by the 18th century B. Krupp described in his book " Echoes of the Ancient Skies " Dover, , "The stars and planets were often a target of worship, believed to represent their gods.
Celestial mechanics thusly became the study of how things move about the heavens. The ancient Greeks were the first to consistently seek natural as opposed to supernatural explanations.
A particularly tenacious set of wrong ideas centered on motion, which for nearly years built on the work of Aristotle B. This work, dubbed "the theory of impetus," would undergo major revisions in the sixth, 12th and 14th centuries A. Terrestrial mechanics thusly became the study of how things move and interact on the Earth's surface. By the 16th century, scholars began to notice that the theory of impetus was ill suited for describing many phenomena — in particular, projectiles flung from catapults and cannons.
Classical Mechanics, Philosophy of
According to the theory, a projectile should fly through the air until it runs out of impetus, whereupon it should fall straight to the ground. In reality, the path of a projectile is a very specific curve. To make sense of these observations, according to Bernard Cohen in " The Birth of a New Physics " Norton, , scientists began to think about gravity pulling on objects with uniform acceleration.