A double pendulum is a mathematical pendulum with another pendulum attached to its loose end (see sketch). We will consider here a horizontal double pendulum where the arms run in a horizontal plane perpendicular to gravity. Moreover, we will control the position of the outer pendulum by a motor such that the angle between the x-axis and the outer arms revolves with with a fixed, constant frequency N. a) Label the quantities in the sketch: The pendulum is moving in the (x, y) plane. How is gravity oriented? The inner arm has length R. Its fixed end lies in the origin of the (x, y)-plane, and it is pointing in direction (t) with respect to the positive x axis. The outer arm has a length L. It connects the loose end of the inner arm and a weight of mass M. The angle between this arm and the r-axis is t. Q b) Consider the vectors (o) = x cos + sino and (0) = f(o). Show that for each value of they form an orthonormal pair of unit vectors in the (x, y)-plane.