Extra-Material-Free-Precession-of Earth

E along the axis of rotation hence we can write 497

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Unformatted text preview: as seen in the fixed frame. http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node71.html#e9.89 Page 1 of 5 Euler angles 11/6/13 1:39 AM The second rotation is counterclockwise (if we look down the axis) through an angle The new frame has coordinates , , , and unit vectors , , about the -axis. . By analogy with Equation (496), the transformation of coordinates can be represented as follows: (498) The angular velocity vector associated with has the magnitude , and is directed along (i.e., along the axis of rotation). Hence, we can write (499) The third rotation is counterclockwise (if we look down the axis) through an angle about the new frame is the body frame, which has coordinates , , , , and unit vectors , -axis. The . The transformation of coordinates can be represented as follows: (500) The angular velocity vector associated with axis of rotation). Note that has the magnitude , as the third rotation is about , and is directed along (i.e., along the . Hence, we can write (501) Clearly, is minus the precession rate about the -axis, as seen in the body frame. http://farside.ph.utexas.edu/teaching/celestial/Celestialhtml/node71.html#e9.89 Page 2 of 5 Euler angles 11/6/13 1:39 AM The full transformation between the fixed frame and the body frame is rather complicated. However, the...
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This document was uploaded on 01/22/2014.

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