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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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Hertz on the Hamilton formalism

Hertz on the Hamilton formalism

Chapter:
(p.247) 23 Hertz on the Hamilton formalism
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0023

In the introduction to his book Principles of Mechanics, Heinrich Hertz emphasised that one of the advantages of his geometric formulation of his mechanics is that it throws a bright light upon William Rowan Hamilton's method of treating mechanical problems by the aid of characteristic functions. Hertz developed the geometric version of the Hamilton formalism in the first kinematic book and then applied these results to the motion of free holonomic systems, and finally to the motion of unfree systems. Thus, Hertz was able to express the analytical equations of the Hamilton formalism for a conservative system, without taking the hidden system into account except through the force function U. The geometry that made his theory for the straightest distance so appealing no longer holds in his description of conservative systems. However, it is possible to introduce a different metric in configuration space, so that the geometric part of the theory also applies to conservative systems.

Keywords:   Hamilton formalism, William Rowan Hamilton, straightest distance, mechanics, conservative systems, characteristic functions, motion, geometry

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