HW13_prob3_GPS20_G10

HW13_prob3_GPS20_G10 - GPS Problem 8.20 (2nd ed. 8.10)...

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GPS Problem 8.20 (2 nd ed. 8.10) Modi f ed Planar Double Pendulum This problem is a variation of the planar double pendulum problem, illustra- trated in Fig. 1.4. The solution to that problem, GPS 1.22 or 2 nd ed. 1.20, will be useful here. There are two major modi f cations that are required. First, we put m 1 =0 and m 2 = m . Second, the angle θ 1 is now a driven coordinate with a uniform rotation frequency, that will be denoted as ω .S ow eh a v e · θ 1 = ω and θ 1 ( t )= ωt ,w ith θ 1 (0) = 0 for simplicity. The remaining changes are minor: we let l 1 = a , l 2 = l ,and θ 2 = θ . Because the motion of the mass point is con f ned to the vertical plane, the system has only one degree of freedom, described by the angle θ , θ 2 in Fig. 1.4, as the generalized coordinate. The angles will be measured from a y axis that points downwards so that θ 1
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.

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HW13_prob3_GPS20_G10 - GPS Problem 8.20 (2nd ed. 8.10)...

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