Hw6 - Homework 6 Due Tuesday November 3 http nsgsun.aae.uiuc.edu AAE250 1 Use Lagrange's equation to determine the equations of motion for the

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Unformatted text preview: Homework 6 Due Tuesday November 3 http: nsgsun.aae.uiuc.edu AAE250 1. Use Lagrange's equation to determine the equations of motion for the following system: a uniform disk of radius a rolls without slipping on a plane inclined at constant angle . The disk is attached to two supports by springs with constant k1 and k2 . AAE 250 11 00 k1 11 00 1 g 0 111111111111111111111 000000000000000000000 11 00 111111111111111111111 000000000000000000000 1 0 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 1111 0000 m 1 0 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 1 0 1111 0000 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 1111 11 0000 00 111111111111111111111 000000000000000000000 a 111111111111111111111 000000000000000000000 11 11111 00 00000 k 2 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 11 11111 00 00000 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 11111 00000 111111111111111111111 000000000000000000000 111111111111111111111 000000000000000000000 11111111111111111111111 00000000000000000000000 111111111111111111111 000000000000000000000 11 00 11111111111111111111111 00000000000000000000000 111111111111111111111 000000000000000000000 11 00 11111111111111111111111 00000000000000000000000 111111111111111111111 000000000000000000000 11 00 11111111111111111111111 00000000000000000000000 111111111111111111111 000000000000000000000 11 00 2. Solve Problem 6-9 from Greenwood, and in addition: a Is the Jacobi integral h de ned in Section 6-8 constant? b Is h = T + V ? c Determine expressions for T and V de ned in Section 6-8 such that h = T +V 0 0 0 0 3. Solve Problem 6-10 from Greenwood, and determine expressions for all available constants of the motion for the nonlinear system. 1 ...
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This document was uploaded on 04/25/2011.

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