Extra-Material-Free-Precession-of Earth

Hence the components of the angular velocity vector

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Unformatted text preview: 8) (489) and (490) where (491) We conclude that, in the body frame, the angular velocity vector precesses about the symmetry axis (i.e., the -axis) with the angular frequency . Now, the components of the angular momentum vector are (492) (493) http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node70.html#e9.73a Page 3 of 4 Euler's equations 11/6/13 1:42 AM and (494) Thus, in the body frame, the angular momentum vector is also of constant length, and precesses about the symmetry axis with the angular frequency . Furthermore, the angular momentum vector subtends a constant angle with the symmetry axis, where (495) The angular momentum vector, the angular velocity vector, and the symmetry axis all lie in the same plane; that is, , as can easily be verified. Moreover, the angular momentum vector lies between the angular velocity vector and the symmetry axis (i.e., ) for a flattened (or oblate) body (i.e., ), whereas the angular velocity vector lies between the angular momentum vector and the symmetry axis (i.e., ) for an elongated (or prolate) body (i.e., ). (See Figure 31.) Next: Euler angles Up: Rigid body rotation Previous: Principal axes of rotation Richard Fitzpatrick 2013-06-15 http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node70.html#e9.73a Page 4 of 4 Euler angles...
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This document was uploaded on 01/22/2014.

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