Given initial conditions and equations for translational acceleration; Euler angle change over time; body angular accelerations; roll, pitch and yaw moments; and angular velocities, ODE45 was utilized to numerically determine the motion of the quadcopter over a given simulation time. Since ODE45 requires first-order ODEs, several equations of motion had to be reduced from second-order. This, in addition to the fact that many variables show up across multiple equations, a state space was created. The velocities of the four motors changed over the simulation time, resulting in different rotations, so each time frame had to be calculated separately. The position, velocity, and rotation of the quadcopter was then graphed over time. The case in which the forces of the rotors were described by different equations as per an autopilot was also analyzed. This was used to help the unstable quadcopter stabilize over time.