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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 principles of mechanics before Hertz

The principles of mechanics before Hertz

Chapter:
(p.8) 2 The principles of mechanics before Hertz
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0002

The period until 1860 saw a steady flow of interesting new theoretical discoveries in mechanics, even in the area of mechanics of systems of finitely many mass points. Moreover, there was a continued discussion about the meaning, nature, and foundations of the principles of mechanics and the concepts entering into them. These discussions went on till well into the 20th century, and provide the background and the mechanical context for Heinrich Hertz's book (Principles of Mechanics). This chapter presents the most important elements of this mechanical context for Hertz's work. First, the development of mechanics from Isaac Newton to Hertz is summarised, focusing on the different laws and principles of mechanics discussed by Hertz. Newton's laws of motion are examined, along with the principle of virtual work, d'Alembert's principle, Lagrange multipliers, principle of live force, principle of conservation of energy, Gauss's principle of least constraint, Jacobi's version of the principle of least action, Hamilton's equations of motion, and basic notions of mechanics. A terminology of concepts such as mass, space, time, distance, and force is also presented.

Keywords:   mechanics, laws of motion, Isaac Newton, basic notations, principles of mechanics, virtual work, conservation of energy, Lagrange multipliers

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