Compare Probs.1 and 2 in matrix form and indicate the type of coupling present in each coordinate system.
Problem 1
Assuming small amplitudes, set up the differential equations of motion for the double pendulum using the coordinates shown in Figure. Show that the natural frequencies of the system are given by the equation
Determine the ratio of amplitudes X1/X2 and locate the nodes for the two modes of vibration.
Problem 2
Set up the equations of motion of the double pendulum in terms of angles θ1 and θ2 measured from the vertical.