An elementary treatise on analytic mechanics : With numerous examples (1912)
Bowser, Edward A. (Edward Albert), 1845-1910 · New York : D. Van Nostrand · leaf 244
e particle, P,on which the value of theattraction is required, to beoutside the shell. Let p and k be the densityand thickness of the shell, 0its centre, and M any particle of it. Let OM = a,PM = r, OP = c, the angle MOP = 0, <p the angle whichthe plane MOP makes with a fixed plane through OP.… … therefore the attraction of M on P, resolved along 0P9 _ pk a2 sin 0 dd d(p c — a cos 0r2 r We shall eliminate 0 from this equation by means of/■a = a2 + c2 — 2ac cos $;.•. rdr = ac sin 6 dd: (i) SPHERICAL SHELL. 227 .. sin Odd = , ac 7*^ -4~ C^ — cfi and c — a cos 0 = —-~ ~; 2c substituting these…
Mechanics, Analytic
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