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Recall the simple double pendulum considered in Example 8.9. We now explore some solutions to the equations of motion developed in the text.
a. Write a matlab function that accepts as inputs l1, l2, mP , mQ, a time span (initial and final times), and initial conditions for θ1, θ2, 1, and 2 and integrates the equations of motion of the simple double pendulum for these values over the specified time span.
b. Integrate the equations of motion for mP = mQ = 4 kg, l1 = l2 =1 m, and initial conditions such that the pendulum starts from rest with both arms extended horizontally to the right of the attachment point (i.e., θ1(0) = θ2(0) = π/2). Plot the first 10 s of the resulting trajectories of points P and Q on one graph, using coordinates in the D = (O, ex, ey, ez) frame, where ex = e2 and ey = −e1 (these would be the paths you observed the particles tracing out if you were observing the double pendulum in action). Repeat the integration for initial conditions with the first link as before and the second link starting pointing up, perpendicular to the first (i.e., θ2(0) = −π).
c. Perform integrations with unequal masses and link lengths. Explain how these differences affect the behavior of the double pendulum.

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