One type of these devices with a rotating base and underactuated arm that was developed by Katsuhisa Furuta is a common test case in nonlinear control theory. One of these systems is suspended from a V-shaped pair of strings that draw Lissajous (10[2])(“lee-sa-ZHOO”) curves (10[2])in a (10[1])harmonograph. (10[5])A simple feedback (10[2])control system can be used to keep an upside-down one of these (10[2])devices (10[4])stable (10[1])atop a cart. (10[4])If 3 (10[1])cosine theta-one (10[1])plus (10[1])cosine (10[1])theta-two is greater (10[1]-5[1])than 2, a flip cannot occur in coupled (10[1])“double” (10[2])examples (10[2])of these systems (10[4])that exhibit (10[2])chaotic motion. (10[1])Under the (10[1])small angle approximation, these systems exhibit motion with a period (10[1])proportional to the square root of L over g, (10[1])acting (10[1])as a simple harmonic oscillator. For 10 points, name these systems consisting of a mass suspended at the end of a rod. ■END■