 A lamina is bounded on two sides by two similar ellipses, the ratio of the axes in each being m, and on the other two sides by two similar hyperbolas, the ratio of the axes in each being n. These four curves have their principal diameters along the coordinate...  The Analyst - Page 1721882Full view - About this book
 | Edward John Routh - Dynamics - 1877 - 688 pages
...with regard to xy. This gives at once A + B= } /Ydudp, where the limits are clearly u = ^ to Ex. 5. A lamina is bounded on two sides by two similar ellipses,...the axes in each being m, and on the other two sides bytwo similar hyperbolas, the ratio of the axes in each being n. These four curves have their principal... | |
 | Mathematics - 1881 - 608 pages
...: On a line whose length is a are two points ./• distance apart; what is the average value of a;? 440 Selected. — A lamina is bounded on two sides...the product of inertia about the coordinate axes is where aa', ftft' are the semi-major axes of the curves. (Routh's Rigid Dynamics.) PUBLIC A TIONS RECEIVED.... | |
 | Edward John Routh - Dynamics, Rigid - 1882 - 408 pages
...A. + B = \ [fdudv, where the limits are clearly u = ^ o'! to y , r = /3t to v=ff*. Ex. 5. A lamiua is bounded on two sides by two similar ellipses, the...that the product of inertia about the co-ordinate (a* - a") (8* - B^) axes is ; — ZTTt a)" ' w^ere aa', 13/3' are the semi-major axes of the curves.... | |
 | Edward John Routh - Dynamics, Rigid - 1891 - 442 pages
...gives at once A + D = \ffdudv, where the limits are clearly 11 = ^0.to 4o'3, »=j82 to t's/S*. Ex. 5. A lamina is bounded on two sides by two similar ellipses, the ratio of the axes in each being HI, and on the other two sides by two similar hyperbolas, the ratio of the axes in each being n. These... | |
 | Edward John Routh - Dynamics, Rigid - 1897 - 460 pages
...gives at once A+B=\Jfdiidr, where the limits are clearlyu=lo a tou = 4a' 2 , c=j3 2 to v=/3f*. Ex. 5. A lamina is bounded on two sides by two similar ellipses,...the product of inertia about the co-ordinate axes is -—rv-y^—Si r^. where a, a'; fl, B' are the semi-major axes of the curves. 4 (m- + n-) (a 2 - a'... | |
 | George William Hill - 1908 - 86 pages
...Analyst, Des Moines, 10, 1883, pp. 65-66. Reviewed in Sidereal Messenger, 2, 1883-84, p. 132. 278. "A lamina is bounded on two sides by two similar ellipses,...diameters along the co-ordinate axes. Prove that the (O2 a'2) («2 fl") product of inertia about the co-ordinate axes is -r-. — , , ,. — 4 (»«* +... | |
 | National Academy of Sciences (U.S.) - Scientists - 1909 - 528 pages
...Analyst, Des Moines, 10, 1883, pp. 65-66. Reviewed in Sidereal Messenger, 2, 1883-84, p. 132. 278. "A lamina is bounded on two sides by two similar ellipses,...diameters along the co-ordinate axes. Prove that the (Oa _a'2) (fl> _«'») product of inertia about the co-ordinate axes is ~Ti — i _il i \ where oa',... | |
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