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Mechanistic Images in Geometric FormHeinrich Hertz's 'Principles of Mechanics'$
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Jesper Lützen

Print publication date: 2005

Print ISBN-13: 9780198567370

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198567370.001.0001

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A history of non-holonomic constraints

A history of non-holonomic constraints

(p.240) 22 A history of non-holonomic constraints
Mechanistic Images in Geometric Form


Oxford University Press

Heinrich Hertz was not the first to introduce non-holonomic constraints into mechanics, but his careful distinction between holonomic and non-holonomic constraints in his book Principles of Mechanics influenced the general history of that discipline. This chapter provides a brief history of non-holonomic constraints and Hertz's place in it. The immediate reaction to Hertz's book is first discussed, and a general overview of the very messy history of repeated independent mistakes, rejections, and rescues is then presented. Hertz derived various integral principles such as the principle of least action and Hamilton's principle for holonomic conservative systems, but concluded that these principles are invalid for non-holonomic systems. This had devastating effects on the energetic image because it meant that its fundamental law, Hamilton's principle, was, in fact, incorrect for a wide variety of mechanical systems. This was one of Hertz's major reasons for rejecting that image. The situation called for an immediate rescue operation. The operation was led by the mathematician Otto Hölder.

Keywords:   non-holonomic constraints, mechanics, rejections, mistakes, rescues, Hamilton's principle

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