Encyclopaedia Britannica, 11th Edition, Volume 8, Slice 9

Dyer to Echidna

Author: Various Authors
Published: 1911
Language: English
Wordcount: 165,558 / 520 pg
Flesch-Kincaid Reading Ease: 71.7
LoC Category: AE
Downloads: 638
Added to site: 2011.06.12
mnybks.net#: 30137
Genre: Reference
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Excerpt

the whole subject it is convenient to deviate somewhat from the historical order of development, and to begin with the consideration of impulsive motion. Whatever the actual motion of the system at any instant, we may conceive it to be generated instantaneously from rest by the application of proper impulses. On this view we have, if x, y, z be the rectangular co-ordinates of any particle m,

mx` = X', my` = Y', mz` = Z', (2)

where X', Y', Z' are the components of the impulse on m. Now let [delta]x, [delta]y, [delta]z be any infinitesimal variations of x, y, z which are consistent with the connexions of the system, and let us form the equation

[Sigma]m(x`[delta]x + y`[delta]y + z`[delta]z) = [Sigma](X'[delta]x + Y'[delta]y + Z'[delta]z), (3)

where the sign [Sigma] indicates (as throughout this article) a summation extending over all the particles of the system. To transform (3) into an equation involving the variations [delta]q1, [delta]q

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