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Unformatted text preview: following results can easily be verified:
(503) It follows from Equation (502) that
- and . In other words, is the angle of inclination between the -axes. Finally, because the total angular velocity can be written (504) Equations (497), (499), and (501)-(503) yield (505)
and The angles (507) , , and precession about the
body frame, and are termed Euler angles. Each has a clear physical interpretation:
-axis in the fixed frame, is minus the angle of precession about the is the angle of inclination between the components of the angular velocity vector - and is the angle of
-axis in the - axes. Moreover, we can express the in the body frame entirely in terms of the Eulerian angles, and their time derivatives [see Equations (505)-(507)].
Consider a freely rotating body that is rotationally symmetric about one axis (the -axis). In the absence of an external torque, the angular momentum vector is a constant of the motion [see Equation (455)]. Let
point along the -axis. In the previous section, we saw that the angular momentum vector subtends a
constant angle with the axis of symmetry; that is, with the http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node71.html#e9.89 -axis. Hence, the time derivative of the Page 3 of 5 Euler angles 11/6/13 1:39 AM Eulerian angle is zero. We also saw t...
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