A treatise on gyrostatics and rotational motion . The numerator of the first fraction is 2T, the denominator by the equationof the [Ax2 + By2 + Cz2 = k*, where, taking the mass of the body asunity, we must suppose h a length to keep the dimensions right in formulaewhich follow] is k*. Hence we have J*. = ** (4) a constant. Thus w varies as OP. We have seen that 00 cos LOI = 2T/H. Hence (4) gives cos LOI = fypr, J, (5) If we take the second relation in (3), A2y>2 + B2g2 + C2r2_ o>2 (n A2x2 + B2y2+C2z2~ OP2 we notice that the perpendicular from the centre 0 to the tangent plane,which
A treatise on gyrostatics and rotational motion . The numerator of the first fraction is 2T, the denominator by the equationof the [Ax2 + By2 + Cz2 = k*, where, taking the mass of the body asunity, we must suppose h a length to keep the dimensions right in formulaewhich follow] is k*. Hence we have J*. = ** (4) a constant. Thus w varies as OP. We have seen that 00 cos LOI = 2T/H. Hence (4) gives cos LOI = fypr, J, (5) If we take the second relation in (3), A2y>2 + B2g2 + C2r2_ o>2 (n A2x2 + B2y2+C2z2~ OP2 we notice that the perpendicular from the centre 0 to the tangent plane,which touches the at the point P in which it is intersected by the ,. Fig. 107 has cosines proportional to , By, Cz, that is to Ap, Bq, Cr. The perpen-dicular therefore coincides with the fixed line OH. Its length — isl-i/{+B1>r + C-z-)h, that is by ((J) /.Vn (H . OP), =/,-(2T) 11. which isconstant. Thus the always touches a plane perpendicular to the axis xxi THE POINSOT MOTION OF A TOP 447 of resultant .-a the constant distance Jt?(2Ty II Erom the centre of theellipsoid. A. plane through 0 parallel to the plane just determined |s calledthe invariable plain (). In tbi* plane an impulsive couple, of momentII. would have to be laid to produce the motion Erom rest. The fixed lineOL is called the invariable line (hi.). [See Fig. L07, in which OH coincideswith OL and OP is the radius vector of the momenta! ellipsoid whichcoincides with 01.] 3. Measurement of tin tirm of motion. Sylvester8 theorem. The turning about 01, which is coincident with OP. At P the touchesa plane parallel to the LP., and so rolls on that plane.
Size: 1951px × 1281px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, bookidtreatiseongyrost00grayric
