A treatise on gyrostatics and rotational motion . w = 0 (2) The angular momenta about 0(D, E, C) are At), A\jramd, Cn+K,so that the components about <»(.//:) are /<x = (C/cosfhsin6\ //„ = Ar), fcz=A^sin20+(C%+K)cose. (3)Clearly //. is a constant: in what follows we shall denote it by 350 GYROSTATICS chap. (4) .(6) The equations of motion are M(w -yjsv) = X, M I v + yjm) = Y, 1 hx — \fshy = a Y. hy + yphx= — X, Y we obtain hx—\frhy=all(v+\fnb), hy+\j/hx= —aM.(u—\jsv), (5) which may be written jXhx+aW<faine)-yir(hy+aWe)=0, Equations (6) are obviously true. The angula
A treatise on gyrostatics and rotational motion . w = 0 (2) The angular momenta about 0(D, E, C) are At), A\jramd, Cn+K,so that the components about <»(.//:) are /<x = (C/cosfhsin6\ //„ = Ar), fcz=A^sin20+(C%+K)cose. (3)Clearly //. is a constant: in what follows we shall denote it by 350 GYROSTATICS chap. (4) .(6) The equations of motion are M(w -yjsv) = X, M I v + yjm) = Y, 1 hx — \fshy = a Y. hy + yphx= — X, Y we obtain hx—\frhy=all(v+\fnb), hy+\j/hx= —aM.(u—\jsv), (5) which may be written jXhx+aW<faine)-yir(hy+aWe)=0, Equations (6) are obviously true. The angular momenta about horizontalaxes parallel to Ox, Oy and drawn through the point of contact with thetable are hx + Ma20 sin 6, h^ + Mo-d respectively, and the t< »tal rates of growthof about them are the expressions on the left of (6), which are zer. sinceno couples act about these axes. The second equation of (6) is important, and can be establish^! at once asfollows. Written in full it is (A + Ma-)e + (Cn + K + M«2>i)^ sin 0-(A + Ma2 )vV=sin 0 cosO = 0. ...i 7)If we write the second and third terms as (Cn + K + Ud-,/> sin-tf)x/r sin 6-(Av> sin 0- M,/-,/sin # cos Q) \! cos &we see at once, by taking axes 0(D, E, C) through the point of contact Op
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