**Unformatted text preview: **z-axis along the symmetry axis of the rod equals J = ml 2 3 ml 2 3 ⇒ J = ml 2 3 ( ω 1 e x + ω 2 e y ) Furthermore, c = l 2 e z , v = u + ω × l e z . 4. A line passing through the center of mass is a principal axis if it is parallel to a vector v = v 1 e x + v 2 e y + v 3 e z such that J v 1 v 2 v 3 = λ v 1 v 2 v 3 for some λ . The moment of inertia matrix about a point shifted by a vector v from the center of mass is then given by J + m v 2 2 + v 2 3-v 1 v 2-v 1 v 3-v 1 v 2 v 2 1 + v 2 3-v 2 v 3-v 1 v 3-v 2 v 3 v 2 2 + v 2 3 and v 2 2 + v 2 3-v 1 v 2-v 1 v 3-v 1 v 2 v 2 1 + v 2 3-v 2 v 3-v 1 v 3-v 2 v 3 v 2 2 + v 2 3 v 1 v 2 v 3 = . 1...

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- Spring '08
- Weaver
- Inertia, Moment Of Inertia, Rigid Body, inertia matrix