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 ωsuch 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 mattached to their ends. Both joints shown in the figure are frictionless. The external force Fencloses a fixed angle γwith 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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