dyn2 - and . Find the constraint forces. Is the system...

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2.032 DYNAMICS Fall 2004 Problem Set No. 2 Out: Wednesday, September 22, 2004 Due: Wednesday, September 29, 2004 at the beginning of class Problem 1 Show that for any 3 × 3 skew-symmetric matrix A , there exists a 3-dimensional vector ω such that for any three-dimensional vector x , Ax = ω × x . Problem 2 Consider the coupled pendula shown in the figure below. Both rods are massless, with point masses m attached to their ends. Both joints shown in the figure are frictionless. The external force F encloses a fixed angle γ with the line of the pendulum shown. The masses never collide. The constant of gravity is g. Questions: Identify the constraints. Determine the number of degrees of freedom. Find the equations of motion for
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Unformatted text preview: and . Find the constraint forces. Is the system conservative? (Why?) m F m l 1 l 2 l 3 g Problem 3 Determine the angular velocity of a cone rolling on the XY -plane without slipping, as shown. Figure by OCW. Problem 4 (adapted from Ginsberg, 3-22) The disk rotates at 1 about its axis, and the rotation rate of the forked shaft is 2 . Both rates are constant. Determine the velocity and acceleration of an arbitrarily selected point B on the perimeter. Describe the results in terms of components relative to the xyz axes in the sketch. x 1 y A B 2 z q w Figure by OCW. After 3-22 in Ginsberg, J. H. Advanced Engineering Dynamics. 2nd ed. New York: Cambridge University Press, 1998....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.032 taught by Professor Georgehaller during the Fall '04 term at MIT.

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dyn2 - and . Find the constraint forces. Is the system...

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