E40  De minimis oscillationibus corporum tam rigidorum quam flexibilium. Methodus nova et facilis.
(On the smallest oscillations of rigid and flexible bodies. A new and easy method.)
Summary:
(based on C. Truesdell's An idiot's fugitive essays on science: methods, criticisms, training,
circumstances)
This is Euler's first paper on vibrating bars. He integrates the equation k^{4}y''' = y
using power series.
It may have been presented to the St. Petersburg Academy on October 27, 1735.
Publication:

Originally published in Commentarii academiae scientiarum Petropolitanae 7, 1740, pp. 99122

Opera Omnia: Series 2, Volume 10, pp. 17  34
 Reprinted in Comment. acad. sc. Petrop. 7, ed. nova, Bononiae 1748, pp. 90112 + 2 diagrams
[E40a]
Documents Available:
 Original publication: E040 (in the Commentarii)
 An article about the
physics
of music
 The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E40 include:
 Katz VJ., “The calculus of the trigonometric functions.” Historia Mathematica, 14 (4), pp. 311324 (Nov 1987).
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