Question 1: Equations of motion of lateral dynamics (%50) Suppose a missile flies in the horizontal plane with velocity Vb = as shown in the figure. Here uo is constant, but v is variable, is heading (yaw) angle, r is yaw rate, N is aerodynamic moment in z, direction, Ay is aerodynamic force in y, direction, Sr is rudder angle, T is thrust and a+ is thrust misalignment angle and L is distance between c.g. and missile's motor. Models of yaw moment and side force are: N=No+N+ Nr + Ng,r =A+ A+ Asror Ay Here No. No. Nr. Nor. Ao. A. Agr. ar. L and to are supposed to be constants. We assume m is mass and I, is moment of inertia about z axis. North A) Drive equations of motion. (use force in y, direction in and moment in z, direction). B) Write equations of motion in state space form. Suppose that x=[],u=[] C) Linearize equations of motion and write them in state-space form. Suppose that Ax= D) Optain the natural frequency and damping ratio of the system. Au