An Expedition to Continuum Theory by Wolfgang H. Müller

Author:Wolfgang H. Müller
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

(8.5.12)

Why do the symbols , , and f carry no dashes? Note that the expressions , , , and are known as Coriolis force, centrifugal force, Euler force, and force of relative translation, respectively. They are all inertia forces.

Instead of using the term fictitious forces one should rather talk of inertia forces (cf., Meriam (1978), p. 201), since this is exactly what these system dependent forces are: Masses seem to have a certain perseverance to remain in their original state of motion. In other words they are “inert” and in order to accelerate them or to change the course of their motion forces are required. This was Newton’s great discovery. At the beginning of his famous book Philosophiae Naturalis Principia Mathematica (1726)2 (Mathematical Principles of Natural Philosophy) he distinguishes in the Definitiones two kinds of forces. On the one hand side there is the vis insita, in other words a force proper to matter, which we call inertia force today (with the exception of the sign):

Definitio III. Materiae vis insita est potentia resistendi, qua corpus unumquodque, quantum in se est, perseverat in statu suo vel quiescendi vel movendi uniformiter in directum. (Definition III. The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line.)

On the other hand side there is the vis impressa (in other words: an “applied” force, which comes from outside and which belongs on the right hand side of the momentum balance):

Definitio IV. Vis impressa est actio in corpus exercita, ad mutandum ejus statum vel quiescendi vel movendi uniformiter in directum. (Definition IV. An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line.)

It becomes particularly fascinating when Newton explains in his fifth definition the notion of a centripetal force for the first time, since his centripetal force is not what we mean by that term today, i.e., not :

Definitio V. Vis centripeta est, qua corpora versus punctum aliquod, tanquam ad centrum, undique trahuntur, impelluntur, vel utcunque tendunt. (Definition V. A centripetal force is that by which bodies are drawn or impelled, or any way tend, towards a point as to a centre.)

He continues to explain and says: Hujus generis est gravitas, qua corpora tendunt ad centrum terrae; vis magnetica, qua ferrum petit magnetem; …. Lapis, in funda circumactus, a circumagente manu abire conatur; & conatu suo fundam distendit, eoque fortius quo celerius revolvitur; &, quamprimum dimittitur, avolat. Vim conatui illi contrariam, qua funda lapidem in manum perpetuo retrahit & in orbe retinet, quoniam in manum ceu orbis centrum dirigitur, centripetam appello. (Of this sort is gravity, by which bodies tend to the centre of the Earth; magnetism, by which iron tends to the loadstone; …. A stone, whirled about a sling, endeavours to recede from the hand that turns

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.