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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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Connections. Material systems

Connections. Material systems

Chapter:
(p.187) 15 Connections. Material systems
Source:
Mechanistic Images in Geometric Form
Author(s):

JESPER LÜTZEN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567370.003.0015

Any image of mechanics must be able to account for interactions between different parts of a system. In the ordinary image, interactions are caused by forces, in Heinrich Hertz's image they are due to constraints or connections. Hertz allowed actions at a distance in his image. According to Hertz, connections are purely geometric properties of material systems, not a kinematical or dynamical property. They are what Hertz sometimes called rigid connections. When dealing with non-isolated systems, Hertz allowed the connections to depend explicitly on time, but his most fundamental considerations concerned systems where the connections are independent of time, so-called normal connections. It is the purely geometric nature of the connections that makes them less objectionable to Hertz than forces. This chapter discusses Hertz's derivation of the equations of connection and the distinction between holonomic and non-holonomic systems.

Keywords:   mechanics, connections, rigid connections, normal connections, forces, holonomic systems, non-holonomic systems, material systems, image

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