An elementary treatise on theoretical mechanics (1893)
Ziwet, Alexander, 1853-1928 · New York, London, Macmillan and Co. · leaf 39
warpedquadrilateral (hyperbolicparaboloid) ^^CZ?. The latteris generated by the line LMgliding along AB and CD soas to remain parallel to theplane yz. The data are OA =CD=a, OB=b, OC=AD=c.We take as element aninfinitesimal prism PQ of base dxds and height y. From similar triangles we have y/RL =… … Fig. 13. J\{a-x)dx |-| ^ J (a —x) dx c^0 22 y = - n° ,a—x c—z J Jb —- dxdza c 2ac fia-x)•/o dx ■ ii^ a-3 ~a a^- Finally, z = \c, by analogy with x. S3-] DETERMINATION OF CENTROIDS. 29 53. Exercises. (i) Three beads of masses 3, 5, 12, are strung on a straight wirewhose mass is neglected, the bead…
Mechanics, Analytic
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