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Unformatted text preview: hat the angular momentum vector, the axis of symmetry, and the angular velocity vector are coplanar. Consider an instant in time at which all of these vectors lie in the
plane. This implies that
constant angle
gives  . According to the previous section, the angular velocity vector subtends a with the symmetry axis. It follows that and . Equation (505) . Hence, Equation (506) yields
(508) This can be combined with Equation (495) to give (509) Finally, Equation (507), together with Equations (495) and (508), yields (510) A comparison of this equation with Equation (491) gives (511) Thus, as expected, is minus the precession rate (of the angular momentum and angular velocity vectors) in the body frame. On the other hand,
axis) in the fixed frame. Note that is the precession rate (of the angular velocity vector and the symmetry
and are quite dissimilar. For instance, http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node71.html#e9.89 is negative for elongated Page 4 of 5 Euler angles bodies (
as 11/6/13 1:39 AM ) whereas is positive definite. It follows that the precession is always in the same sense in the fixed frame, whereas the precession in the body frame is in the opposite sense to for elongated bodies. We found, in the previous section, that for a flattened body the angular momentum vector
lies between the angular velocity vector and the symmetry axis. This means that, in the fixed frame, the
angular velocity vector...
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This document was uploaded on 01/22/2014.
 Winter '14
 mechanics, Inertia

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