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Unformatted text preview: and the symmetry axis lie on opposite sides of the fixed angular momentum vector,
about which they precess. (See Figure 31.) On the other hand, for an elongated body we found that the
angular velocity vector lies between the angular momentum vector and the symmetry axis. This means that,
in the fixed frame, the angular velocity vector and the symmetry axis lie on the same side of the fixed angular
momentum vector, about which they precess. (See Figure 31.) (Recall that the angular momentum vector, the
angular velocity vector, and the symmetry axis are coplanar.) Figure: A freely rotating object that is elongated along its axis of
symmetry,
(left), and a freely rotating object that is flattened
along its axis of symmetry (right). The vector is fixed. Next: Free precession of Earth Up: Rigid body rotation Previous: Euler's equations
Richard Fitzpatrick 20130615 http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node71.html#e9.89 Page 5 of 5 Free precession of Earth 11/6/13 1:25 AM Next: MacCullagh's formula Up: Rigid body rotation Previous: Euler angles Free precession of Earth
It is known that the Earth's axis of rotation is very slightly inclined to its symmetry axis (which passes
through the two geographic poles). The angle is approximately
seconds of an arc (which corresponds
to a distance of about on the Earth's surface). The ratio of the terrestrial moments of inertia is about
, as determined from lunisolar precession. (See Appendix...
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This document was uploaded on 01/22/2014.
 Winter '14
 mechanics, Inertia

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