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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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Integral principles

Integral principles

Chapter:
(p.235) 21 Integral principles
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0021

In his book Principles of Mechanics, Heinrich Hertz treats integral principles in three parts. First, he discusses the properties of geodesics and their relation to straightest paths in a purely geometric way. These investigations then form the basis for a discussion of integral principles applied to the motion of free systems, and finally to the motion of conservative systems. Hertz's approach differed from the usual approach in three respects. First, it was based on his geometry of systems of points. Second, it dealt with forces as an indirect result of a coupling of the visible system with a hidden system. Third, it limited the applicability of even the most general of these principles (Hamilton's principle) to special mechanical systems declaring that it was invalid in general. Hertz pointed out that Hamilton's principle and the principle of least action did not apply to non-holonomic systems.

Keywords:   integral principles, geodesics, straightest paths, motion, free systems, conservative systems, forces, Hamilton's principle

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