Newton's problems with rigid body dynamics in the light of his treatment of the precession of the equinoxes
type: Item
instance of: scholarly article
title: Newton's problems with rigid body dynamics in the light of his treatment of the precession of the equinoxes
zbMATH Open document ID: 0919.01004
author: Geoffrey J. Dobson
published in: Archive for History of Exact Sciences
publication date: 1999-08-26T00:00:00Z
review text: ``\dots at last the entire wheelwork became so complicated that only a few could grasp it all, and to those few was attributed an extraordinary degree of learning. This circumstance, together with the religious respect paid in those days to authority, permitted [the book] to appear as undeniable truth \dots'', pp. 37-38 of \textit{O. Dziobek}, ``Mathematical theories of planetary motions''. New York: Dover Publications (1962; Zbl 0113.23801). Newton's \textit{Principia} was heavily scrutinized when it first appeared, and then learned by rote in Cambridge, and now hardly read at all. It is written in a mathematical language now long out of fashion. It contains many sinkholes for the feet of the unwary. It was completed before the principle of angular momentum was fully understood and catechized by Euler, and so contains many expected deficiencies. Contemporaries such as John I and Nicolas Bernoulli pointed some of these out to Newton himself. \textit{G. J. Dobson} here and \textit{R. Weinstock} in ``Newton's \textit{Principia} and inverse-square orbits in a resisting medium: a spiral of twisted logic'', Hist. Math. 25, No. 3, 281-289 (1998), have focussed on two such deficiencies: they are not the first to do so. Dobson attacks, without full mathematical apparatus, an argument of Newton about the precession of the equinoxes. This precession is best expressed by a theory of mechanics including angular momentum, moments of inertia, the torque of forces, moments of momentum, and all the paraphenalia of Euler, d'Alembert and Clairaut of 1745-1755 when a mistake in arithmetic threatened to pull Newton's house down [see \textit{T. L. Hankins}, ``Jean d'Alembert: Science and the Enlightenment''. Oxford: Clarendon Press (1970), pp. 32-33]. Blind acceptance of any master is foolish, and none should be angry at reasoned criticism of the mathematics as is offered by Dobson and Weinstock. Newton uses elementary moments of inertia -- the equatorial ring for the non-spherical part…
Mathematics Subject Classification ID: 01A45
zbMATH DE Number: 1197108
zbMATH Keywords: Newton
zbMATH Keywords: precession
zbMATH Keywords: equinoxes
zbMATH Keywords: rigid body mechanics
zbMATH Keywords: precession of the equinoxes
zbMATH Keywords: moments of inertia
zbMATH Keywords: tides
MaRDI profile type: Publication
full work available at URL: s004070050024
OpenAlex ID: W2087220103
DOI: 10.1007/S004070050024
description: scientific article; zbMATH DE number 1197108