dyn9 - D l F A F B A h h ( t ) ( t ) C m, I C B a b Problem...

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2.032 DYNAMICS Fall 2004 Problem Set No. 9 Out: Wednesday, November 17, 2004 Due: Wednesday, November 24, 2003 at the beginning of class Problem 1 Consider a wheelbarrow with a wheel of negligible mass, as shown in the figure below. The distance between the center of mass C of the wheelbarrow and the center of its wheel D is l . The handles of the wheelbarrow are of length h , and are pushed at their tips by the forces F A and F B . The time-dependent angles between the forces and the handles are given by α ( t ) and β ( t ), respectively. The wheel rolls without slipping. The centroidal moment of inertia and the mass of the wheelbarrow are given by I c and m , respectively. With the position of C and the orientation of the wheelbarrow as generalized coordinates, derive the equations of motion using Lagrange multipliers.
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Unformatted text preview: D l F A F B A h h ( t ) ( t ) C m, I C B a b Problem 2 A cart and a rolling disk are connected by a rigid massless link of length L , as shown in the figure below. The disk rolls without slipping. Use Lagrange multipliers to determine the force in the link. m C L R M h x g Problem 3 Consider the spinning disk on a rotating linkage with torsional spring problem discussed in class. (a) By introducing generalized moments associated with the coordinates and , reduce the set of equations of motions to a single equation of motion for . (b) For p = 0, sketch the trajectories of the above equation on the ( ) phase plane for different values of p , & (select all other parameters to be equal to one)....
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dyn9 - D l F A F B A h h ( t ) ( t ) C m, I C B a b Problem...

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