"[In an Oct. 20, 1742 letter, Daniel Bernoulli] suggests for Euler's consideration the case of a beam with clamped ends, but states that the only manner in which he has himself found a solution of this "idea generalissima elasticarum" is "per methodum isoperimetricorum." He assumes the "vis viva potentialis laminae elasticae insita" must be a minimum, and thus obtains a differential equation of the fourth order, which he has not solved, and so cannot yet shew that this "aequatio ordinaria elasticae" is general.Ew. reflectiren ein wenig darauf ob man nicht konne sine interventu vectis die curvaturam immediate ex principiis mechanicis deduciren. Sonsten exprimire ich die vim vivam potentialem laminae elasticae naturaliter rectae et incurvatae durch \int ds/R^2, sumendo elementum ds pro constante et indicando radium osculi per R. Da Niemand die methodum isoperimetricorum so weit perfectionniret als Sie, werden Sic dieses problema, quo requiritur ut \int ds/R^2 faciat minimum, gar leicht solviren. [Ew. reflect a little on whether one can not deduce the curvature of the bar directly from the principles of mechanics. In the first place I express the actual elastic laminar potential, naturally right and yet curving, by \int ds/R^2, summing the element ds per constant radius of curvature R. Since no one has perfected the isoperimetric method as much as You, So this problem, which requires that \int ds/R^2 be minimum, might be easily solved.]"
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/A_History_of_the_Theory_of_Elasticity_and_of_the_Strength_of_Materials
Revision History
No revisions have been submitted for this quote.
Categories
A History of the Theory of Elasticity and of the Strength of Materials
A History of the Theory of Elasticity and of the Strength of Materials: from Galilei to the Present Time is a two volume set edited and completed by Karl Pearson from notes written by . It was published by Cambridge at the University Press posthumously in Todhunter's name. Volume I. Galilei to Saint-Venant 1639-1850 was first published in 1886. Volume II. Saint-Venant to Lord Kelvin was first published in 1893.
Related Quotes
"Euler takes the case in which forces act at every point of the elastic curve; and he obtains an equation like the fir…"
"It would be a great aid to science, if, at any rate, the innumerable mathematical journals could be to a great extent…"
"In the summer of 1884... the Syndics... placed in my hands the manuscript of the late Dr Todhunter's History of Elast…"
"[I]t was not till I had advanced... into the work that I felt convinced that... the... writer's terminology and notat…"
"[T]he notation and terminology will be found fully discussed in Notes B—D of the Appendix, which I would ask the read…"
"[C]onsistency in [notation and terminology] will be found after the middle of the chapter devoted to Poisson."
"The symbols and terms used in the manuscript are occasionally those of the original memoirs, occasionally those of La…"
"Dr Todhunter's manuscript consists of two distinct parts, the first contains a purely mathematical treatise on the th…"
"The changes I have made in that manuscript are of the following character; the introduction of a uniform terminology …"
"Keeping the twofold object of this work in view I have endeavoured to give it completeness (1) as a history of develo…"