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# dyn8 - Fall 2004 2.032 DYNAMICS Problem Set No 8 Out...

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2.032 DYNAMICS Fall 2004 Problem Set No. 8 Out : Wednesday, November 10, 2004 Due : Wednesday, November 17, 2004 at the beginning of class Problem 1 Reconsider Problem 1 of Quiz No.1. As shown in the figure, the flywheel spins at a constant rate ω 2 , and also rotates about z axis with angular velocity ω 1 that is a function of time. The center of mass of the flywheel is located on the z axis, and the centroidal moments of inertia are I 1 about the spin axis and I 2 transverse to that axis (a) Derive the Lagrangian equations of motion. (b) Find the generalized forces necessary to maintain the motion. 1 1 z Outer gimbal Inner gimbal 2 w q w Figure by OCW.

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Problem 2 (from Doctoral Qualifying Exam 2002) Two identical rigid cylinders, each having radius R and mass m , are linked by a connecting rod of length 3 R and mass M as shown below. A horizontal force F ( t ) is applied to the center of the right cylinder and neither cylinder slips in its rolling motion. In the initial position, the angle θ locating the connecting pin is zero. Derive the Lagrangian equations of motion for this system.
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