The two-wheeled inverted pendulum, albeit more complex in system dynamics, has similar behavior with a pendulum on a cart. the pendulum and wheel dynamics are analyzed separately at the beginning , but this will eventually lead to two equations of motion which completely describe the behavior of the balance Segway. Three bodies were used, the two rotating masses of the wheels and the chassis / person combined body, which was represented using a single point mass at a certain distance from the axle. The latter was possible as it was anticipated that the person would be significantly heavier than base itself.
Firstly the equations of motion associated with the left and right wheels are obtained. Figure 2.2 shows the free body diagram for both wheels. Since the equation for the left and right wheels are completely analogous, only the equation for the right wheel is given.