The double pendulum consists of two rigid rods of length L1 and L2, attached to point masses m1 and m2. The first rod has one end fixed at the origin, and the second end attached to the mass m1, whose location is defined by the angle 01. The second rod connects the masses m1 and m2, where the location of m2 is defined by the angle 02. The force of gravity my acts on these masses in the downward direction. For simplicity, we will assume L1 = 1, L2 = 1, m1 = 1, m2 = 1, g = 1 . We will consider the state of the double pendulum to be defined by two time-dependent function 01(t), and 02(t). It is possible to derive that the motion of the double pendulum is governed by the system of second-order differential equations poo_ -9(2m1 + m2) sin( 01) - mag sin( 01 - 202) - 2sin( 01 - 02)m2((09)2 L2 + (09)2 LI cos( 01 - 02)) L1(2m1 + m2 - m2 cos(2 01 - 202)) 900 2 sin( 01 - 02)((09)2 Li(m1 + m2) + g(m1 + m2) cos( 01) + (02)2 L2m2 cos( 01 - 02)) L2(2m1 + m2 - m2 cos(201 - 202))