An ultralight aircraft consists of the components in table Q2. The component masses and their positions relative to an arbitrary origin are indicated in the table. i) Determine the components of the inertia matrix relative to the centre of mass (work to one decimal place). ii) A pitching moment is applied about the body y-axis, what happens? iii) A rolling moment is applied about the body x-axis, what happens? iv) Determine the orientation of the principal axes of the aircraft. Table Q2: Component mass and (x, y, z) coordinate positions relative to centre of mass. Component mass [kg] (x, y, z) relative to centre of mass[m] 165 Cockpit, undercarriage and engine Fuselage and lift and control surfaces 60 Fuel (0.2, 0, 0.02) (-1.5, 0,-0.73) 50 (0.34, 0, 0.32) (0.50, 0, 0.32) Pilot 80 [8] A single engine aircraft is in a landing approach at flight speed V, dynamic pressure qoo, angle of attack a, sideslip angle . The landing gear are deployed. Landing gear consists of a belly mounted bogey at (x, 2G) relative to the centre of mass and a forward tricycle gear at (xt, ZG). The belly mounted bogey has a drag coefficient Cp, while the forward gear has drag coefficient CDt Aircraft trim following landing gear deployment is achieved by engine thrust, and rudder and aileron deflection. Engine thrust Fp in a direction acts at zp relative to centre of mass, rudder deflection dR causes additional aircraft side force kfindR at location (TR, ZR), aileron deflection da on the wings causes additional wing lift coefficient kada acting at (ya), aircraft lift curve slope is k acting through centre of mass. All positions are relative to centre of mass, and all coefficients are referenced to the wing area Awing. All other aerodynamic forces are unaffected by the landing gear deployment. i) Describe how the aircraft trim state is disrupted by the landing gear deployment. ii) Derive expressions for the aerodynamic forces due to each component above in body axes (you may use small angle assumptions for all angles). iii) Derive expressions for the pitching and rolling moments of these components. iv) Set up expressions that can be used to solve for a trim condition. Do not attempt to solve the equations.