June 7th, 2011

Walter Noll

Читаю любопытные статьи Уолтера Нолла об основаниях механики, который развивает линию Трусделла. Из статьи "On the concept of force" (2007):

When most physicists today hear the term “classical mechanics” , they tend to think of Newtonian particle mechanics. In this context, Wilczek’s statement “Newton’s second law of motion, F = ma, is the soul of classical mechanics”, may have some merit. However, Newtonian particle mechanics is only a very small and relatively trivial part of classical mechanics. When applied to the rest of classical mechanics, Wilczek’s statement is absurd. For example, engineering students often take a course called “Statics”, which deals with forces in systems having no moving parts at all, and hence accelerations are completely absent. The beginning of a textbook on statics often contains a statement of Newton’s laws, but this functions like a prayer before a business meeting; it is almost totally irrelevant to the substance of the subject. The substance of statics consists in singling out parts of the system under consideration by drawing “free-body diagrams”. Engineering students often also take a course called “Dynamics”. Its basic structure differs from the course in statics only by including the inertial forces among the forces considered.
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The concept of a frame of reference is not the same as the concept of a coordinate system, as some people seem to believe. For a precise definition and discussion, see [1] and [2]. I believe that the use of coordinate systems is an impediment to insight in conceptual consideration in all of physics, classical or modern.
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In classical particle mechanics, inertial forces are paramount and the subject would collapse if they were neglected. In continuum mechanics, inertial forces are sometimes unimportant and can be neglected, for example when considering the motion of toothpaste as it is extruded from a tube. The soul of continuum mechanics is the analysis of contact forces. It requires the use of very
sophisticated mathematics.”