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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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Cyclic coordinates

Cyclic coordinates

Chapter:
(p.208) 18 Cyclic coordinates
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0018

In Heinrich Hertz's account of conservative systems, the concept of a cyclic coordinate, and, in particular, what he called an adiabatic cyclical system, enters as an important technical tool. This chapter explains the meaning of these concepts as understood in the ordinary image of mechanics. First, the historical development of the concept and its important mechanical and mathematical properties are discussed. An example of a simple mechanical system that has a cyclic coordinate is then presented. This example is only meant as a didactical device. The chapter concludes by examining Hermann von Helmholtz's use of cyclic motion in his mechanical model of thermodynamics. Helmholtz's papers on this topic are important for the present book because they were the point of departure for Hertz's ideas on cyclic coordinates. This chapter also considers Edward John Routh's modified Lagrangians and J.J. Thomson's equation of hidden cyclic motion.

Keywords:   cyclic coordinates, mechanics, adiabatic cyclical systems, Hermann von Helmholtz, cyclic motion, thermodynamics, Edward John Routh, Lagrangians, hidden cyclic motion

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