An elementary treatise on analytic mechanics : With numerous examples (1912)
Bowser, Edward A. (Edward Albert), 1845-1910 · New York : D. Van Nostrand · leaf 145
-eighth of thesurface of a sphere. Here x* -f f -f z2 = <x\ \ + dx2 + df) ~ («a — x2 — #3)*/■ /* xdxdy SOLID OF REVOLUTION. w First perform the y-integra-tion, x being constant, fromy == 0 to y = LI = y1 =Va2 — x*; the effect will beto sum up all the elementssimilar to pq from H to I.The effect… … Fig. 42. x = yvvi # rfo % .V2 V 5* Jo e/0 (a2 _ 38 _ ^i / -§-7r# dx ffindx = J«. Similarly y = }ff, s = Jtf. 2. Find the centre of gravity of one-eighth of the surface of the sphere if the density varies as the ^-ordinate to any point of it. Here p = \iz. . 4tf - 4a 2a Ms. » = ^; y = -; 8 = y. 85.…
Mechanics, Analytic
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