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Unformatted text preview: TAM 412, Homework 9, Selected answers Harry Dankowicz Mechanical Science and Engineering University of Illinois at Urbana-Champaign [email protected] 1. Introduce five bases, ˜ e , t (1) , t (2) , t (3) , and e , such that ˜ e is fixed relative to the inertial frame, t (1) is fixed relative to the turntable, t (2) and t (3) are fixed relative to the plane through the rod and the vertical axis, and e is fixed relative to the disc and rod assembly. Let θ represent the angle of rotation about the common 3-axis of t (1) relative to ˜ e, such that ˙ θ = Ω. Let ϕ represent the angle of rotation about the common 3-axis of t (2) relative to t (1) . Let t (3) be rotated relative to t (2) about the common 2-axis by an angle- π/ 6. Let α represent the angle of rotation about the common 1-axis of e relative to t (3) . It follows that ˜ e ω e = e 1 2 (Ω + 2 ˙ α + ˙ ϕ ) √ 3 2 (Ω + ˙ ϕ ) sin α √ 3 2 (Ω + ˙ ϕ ) cos α Moreover, the moment of inertia matrix of the disc and rod assembly about the point O relative to the...
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This note was uploaded on 11/17/2011 for the course TAM 412 taught by Professor Weaver during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08