{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

p09fl26 - Lecture 26 Top with gravity(2 Nov 09 A Review...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 26: Top with gravity (2 Nov 09) A. Review: Euler angles 1. Three successive rotations to get to the principal axes of the moment of inertia tensor: (1) by angle α around the original ˆ z = ˆ e 0 3 , (2) rotation by angle β around the new “y” = “2” axis, (3) rotate by angle γ around the new (and final) ˆ z axis ˆ e 3 . 2. The final result after matrix multiplication for the successive rotations C ( γ ) B ( β ) A ( α ) is CBA = C γ C β C α - S γ S α C γ C β S α + S β C α - C γ S β - S γ C β S α - C γ S α - S γ C β S α + C γ C α S γ S β S β C α S β S α C β using a notation C α = cos α , S α = sin α , etc. 3. Express rotation axes in terms of the principal axes (a) Rotation for γ (= symmetry axis of the symmetric top) is ˆ e γ ˆ e 3 . (b) Rotation for α ˆ e α = ˆ e 0 3 and can express that in terms of the final axes by the transform: (so ˆ e 0 3 · ˆ e 3 = C β ) ˆ e α = CBA · 0 0 1 = - C γ S β ˆ e 1 + S γ S β ˆ e 2 + C β ˆ e 3 (c) ˆ e β : ˆ e β = sin γ ˆ e 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}