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An elementary treatise on analytic mechanics : With numerous examples (1912)
Bowser, Edward A. (Edward Albert), 1845-1910 · New York : D. Van Nostrand · leaf 524
by Art. 233, Ex. 14, W 7a5 2a5 (Prices Anal. Mechs., Vol. II, p. 368). 2. A homogeneous sphere rolls down within a rough,spherical bowl; it is required to determine the motion. Let a be the radius of the sphere, and b the radius of thebowl; and let us suppose the sphere to be placed in thebowl at… … = — R sin cf> + /cos <p~, a) m dt2 ~~ R cos 0 -f- F sin <f> — mg (2) EXAMPLES. 50) Also x = (5 — «) sin 0; y = J — (5 — a) cos 0. g = (»-«)-*f+ (*-)-*© (5) ^co80+-Bin0=(*-a)^. (6) ^0 ^2 « (b-a)df2= F— m9 sin ft (7) .Now to determine the angular velocity of the ball, we mustestimate the…Mechanics, Analytic
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