Extra-Material-Free-Precession-of Earth

Htmle989 page 2 of 5 euler angles 11613 139 am the

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: following results can easily be verified: (502) (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) (506) 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...
View Full Document

This document was uploaded on 01/22/2014.

Ask a homework question - tutors are online