Model the simplified Segway Scooter system shown in the figu

Model the simplified Segway Scooter system shown in the figure below (i.e. find the two equations of motion that describe the system dynamics). The cart has mass M, the rod representing the rider has mass m and length L. The point ? has coordinates (x, y), and is relative to point o on the cart. The rod has moment of inertia J? about point ?. Assume no drag on the cart or the rod and assume a gravitational force g acts downward.

a.) HINT: Begin with the free-body diagrams given below and write a horizontal sum-of-forces equation on the cart and a sum-of-torque equation about point ? on the rod. The two resulting equations should be in terms of: u, fx, fy, M, m, L, ?, z, and J?. b) Next, you’ll want to eliminate fx and fy from the equations you obtained in (a).

To do so, start by generating two additional equations by doing a sum-of-forces in the horizontal and vertical direction on the rod.

(c) Then, use the kinematic relationships below to write fx and fy in terms of L, z, and ?. Note that L is a constant, but z and ? are not.

x = z + L/2 sin(?)

y = L/2 cos(?)

(d) Finally, rewrite your two equations of motion from (a) only in terms of: M, m, z, L, J, ?. Linearize your answer by using the small angle approximation

http://tinypic.com/view.php?pic=mj72a0&s=9#.V240xFeDDFI

Solution

you have uploaded some pic which is not visible.