The London, Edinburgh and Dublin philosophical magazine and journal of science . confines himself almost wholly (i.) to showing thatthere are sufficient equations obtainable to determine thecoordinates of the body, and (ii.) to the consideration ofinitial motions. It therefore appeared of interest to examine whether theproblem of the egg could not be completely solved in themost general case. This solution is effected in the following-pages. 2. Let 0 be the point of contact at any time, C the centreof the hemispherical base, and Gr the centre of gravityof the egg. Let OCZ be the vertical throu
The London, Edinburgh and Dublin philosophical magazine and journal of science . confines himself almost wholly (i.) to showing thatthere are sufficient equations obtainable to determine thecoordinates of the body, and (ii.) to the consideration ofinitial motions. It therefore appeared of interest to examine whether theproblem of the egg could not be completely solved in themost general case. This solution is effected in the following-pages. 2. Let 0 be the point of contact at any time, C the centreof the hemispherical base, and Gr the centre of gravityof the egg. Let OCZ be the vertical through 0, OX theprojection of CG, the axis of the body, on the horizontalplane, and OY a perpendicular to OX in this plane. Let00 = a, CG = /i ; let the moment of inertia of the body about * Communicated by Prof. Karl Pearson, The Problem of Columbus. 459 CG be C, and about any perpendicular to OG through G be # and the angular velocity of the plane ZOXabout OZ be ^r. Let R be the normal reaction at 0 andFl5 F2 the components of the friction along OX, OY. Take. GA the perpendicular to GC in the plane ZCG, GB the per-pendicular to this plane, and GC/ the axis of the body asprincipal axes. They will coincide in direction with OX,OY, OZ when 0 = 0. Let the spins of the body round thembe 2, ft>s, and the spins of the axes round their instan-taneous positions be 0l5 62, 03. Also let the velocities of Gparallel to OX, OY, OZ be u, v, Then we have clearly &>! =ft>2 =*1 = e.,= — yfr sin 6 e I ty cos 0 (1) 460 Mr. H. W. Chapman on Also by the modified form of Eulers equations, A —~ — A03co2 4- C62cos = moment of external forces about GA,A~j^—Cj61ujz-{-A0z(d1 — „ „ „ GB, 1!^-A^ + Afe= „ -, „ GO. These give by (1) —A^sm&-2A0yjrcos0 + Cco30 = F2(h + acos0), . (2)A0 + Cft)3^ sin 0- Ayjr2 sin 0 cos 0 = R7i sin 0 — F1 (a + h cos 0), ? • (3)Ca>3 = F2asin<9. . (4) Next consider the accelerations of G referred to OX, OY,OZ. This syste
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