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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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Unfree systems. Forces

Unfree systems. Forces

Chapter:
(p.219) 19 Unfree systems. Forces
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0019

In his book Principles of Mechanics, Heinrich Hertz discussed the motion of unfree systems. He made the crucial assumption that every unfree system is ‘a portion of a more extended free system’ (a so-called partial system). When Hertz considered an unfree system as a part of a free system ‘it is assumed that the rest of the system is more or less unknown, so that an immediate application of the fundamental law is impossible’. The question is then how to take the influence of the rest of the system into account without knowing its motion in detail. Hertz mentioned two cases where this can be done in different ways. In the first case the rest of the system ‘perform a determinate and prescribed motion’. Hertz introduced the term ‘guided system’ for this situation. The second, more important case, concerned ‘systems acted on by forces’.

Keywords:   motion, unfree systems, forces, guided system, mechanics, free systems

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