So, I am having a lot of troubles visualizing the following system.
The point of suspension of a plane simple pendulum of mass m and length l is constrained to move along a horizontal track and is connected to a point on the circumference of a uniform flywheel of mass M and radius a through a massless connecting rod also of length a, as shown in the figure. The flywheel rotates about a center fixed on the track. Find the hamiltonian for the combined system and determine Hamilton's equation of motion.
Here is my idea so first of all I would construct the Lagrangian and then from it I will get the hamiltonian, so for this I need to determine the kinetic energy and the potential energy.
I am having troubles constructing the cartesian coordinates of this thing which the only thing that I need I know how to do everything else.
Is the following correct
$x = l\sin(\theta) - a(\omega)t$? where I measure the angle of the regular m pendulum with respect to vertical and the other one with respect to horizontal ? and $\omega$ is how fast the flywheel rotates.