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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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The line element: The origin of the Massenteilchen

The line element: The origin of the Massenteilchen

Chapter:
(p.146) 12 The line element: The origin of the Massenteilchen
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0012

Heinrich Hertz did not introduce different types of matter in his image of matter, one for each of the chemical elements. However, he chose to build his material particles from infinitely small Massenteilchen, rather than simply taking the material points themselves as the fundamental building blocks. Hertz could simply have defined a material point as a pair consisting of its mass (given as a real number and an arbitrarily chosen unit mass) and a function of time indicating the position of the material point. This chapter examines why Massenteilchen were introduced by looking at how this concept is put to use in the rest of the axiomatic synthetic structure of Hertz's book Principles of Mechanics. It argues that the derivation of the line element in configuration space, which is the basic concept of Hertz's geometric description of mechanics, provides a key to understanding Hertz's choice of his image of matter.

Keywords:   line element, Massenteilchen, mechanics, image, material points, space

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