D’Alembert’s Principle

Jennifer Coopersmith

in The Lazy Universe

Published in print May 2017 | ISBN: 9780198743040
Published online June 2017 | e-ISBN: 9780191802966 | DOI:
D’Alembert’s Principle

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It is explained how the mysterious Principle of Virtual Work in statics is extended to the even more mysterious Principle of d’Alembert’s in dynamics. This is achieved by d’Alembert’s far-sighted stratagem: considering a reversed massy acceleration as an inertial force. A worked example is given (the half-Atwood machine or “black box”). Some counter-intuitive aspects are made intuitive by more examples: the Pluto-Charon system of orbiting planets; Newton’s and then Mach’s explanation of Newton’s bucket. Also, it is demonstrated that the law of the conservation of energy actually follows from d’Alembert’s Principle. The reader is alerted to the astoundingly fundamental nature of d’Alembert’s Principle. It is the cornerstone of classical, relativistic, and quantum mechanics. As Lanczos writes: “All the different principles of mechanics are merely mathematically different formulations of d’Alembert’s Principle”.

Keywords: d’Alembert’s Principle; dynamics; inertial force; Newton’s bucket; Mach; Pluto and Charon; black box; conservation of energy

Chapter.  7426 words.  Illustrated.

Subjects: Astronomy and Astrophysics ; History of Science and Technology

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