Essays in the History of Mechanics [Hardcover]

Clifford A. Truesdell (Author)

Product Details

• Hardcover: 384 pages
• Publisher: Springer-Verlag; 1st edition (June 1968)
• Language: English
• ISBN-10: 0387043675
• ISBN-13: 978-0387043678
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #3,528,368 in Books (See Top 100 in Books)

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4.0 out of 5 stars A critique of overextensions of the epithet "Newtonian", June 6, 2010

By 

Viktor Blasjo - See all my reviews
(REAL NAME)   

This review is from: Essays in the History of Mechanics (Hardcover)

The leitmotif of these essays is a critique of overextensions of the epithet "Newtonian":

"It is [not] the primitive mechanics of Newton ... that we are taught as the most successful, the most thoroughly proved and understood, and the most perfect of the sciences of nature---the prototype and paradigm of a mathematical theory from physical phenomena. Rather, it is the easier parts of the rational mechanics of the Bernoullis, Euler, and their successors." (p. 87)

Indeed, when Euler, in 1750, published for the first time the general vector equation F=ma "as the axiom which 'includes all the laws of mechanics'" (p. 257), he announced this as "a new principle of mechanics"; whereas today of course this is considered the defining emblem of "Newtonian" mechanics.

"The modern student may find it hard to understand how sixty years of experience with special cases had to follow [the Principia] before this simple conclusion, which he is taught to accept unquestioningly in a first course in physics, was seen. ... No-one [during these years] doubted the correctness of 'Newton's second law', at least as a rule for problem-solving, but what no-one saw, until it was shown, was that among all the various mechanical principles then used it was the one which was general: It applies to every part of every system, and more than this, it suffices to get all the equations determining the motion of many systems." (p. 116) "It is an incontestable fact that more than sixty years of research using more complicated methods even for rather simple problems took place before this 'new principle' was seen." (p. 117)

But this is not all. Euler soon changed his mind and reached the conclusion that his "new principle" did in fact not include "all the laws of mechanics" after all. Rather, the law of moment of momentum must be considered an independent, additional law of mechanics, reducible to F=ma only in special cases:

"The tenet that Newton's Laws or the 'Newtonian' equations in any of their forms suffice, can be held only by those who limit their attention to mass-points, rigid bodies, and certain other special systems. ... But in elasticity Newton's laws never have been and never can be sufficient" (p. 260); instead "everyone in the eighteenth century who studied problems of elasticity invoked the principle of moments" (p. 262), which Euler "laid down ... as fundamental and independent" (p. 172).