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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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Free systems

Free systems

Chapter:
(p.202) 17 Free systems
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0017

Heinrich Hertz's strategy for studying the motion of mechanical systems was to deal first with free systems, to which the fundamental law applies, and then with unfree systems considered as subsystems of free systems. This chapter discusses Hertz's treatment of free systems, which he dealt with in two steps. First, he discussed the purely geometric properties of straightest paths, then went on to investigate the dynamic theory — that is, how systems move in time. At each step he deduced the general differential equations, derived differential and integral principles, and dealt with the special phenomena of holonomic systems. Hertz's introduction of the concept of force, which in a sense is the highlight of the physical content of his mechanics, is explored by focusing on the differential equations of motion and those general differential principles of mechanics that follow from them.

Keywords:   free systems, mechanics, straightest paths, dynamic theory, holonomic systems, force, differential equations of motion

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