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18.123 Using the relation given in Prob. 18.121, d

18.123 Using the relation given in Prob. 18.121, determine the period of precession of the north pole of the earth about the axis of symmetry of the earth. The earth may be approximated by an oblate spheroid of axial moment of inertia I and of transverse moment of inertia I9 = 0.9967I. (Note: Actual observations show a period of precession of the north pole of about 432.5 mean solar days; the difference between the observed and computed periods is due to the fact that the earth is not a perfectly rigid body. The free precession considered here should not be confused with the much slower precession of the equinoxes, which is a forced precession. See Prob. 18.117.)Prob. 18.121Show that the angular velocity vectorω of an axisymmetrical body under no force is observed from the body itself to rotate about the axis of symmetry at the constant ratewhere ωz is the rectangular component of ω along the axis of symmetry of the body

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