An airplane with a flexing wing in flight shown in the top sketch can be idealized...

 

 

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An airplane with a flexing wing in flight shown in the top sketch can be idealized by the mechanical model shown in the bottom sketch. L(y) is the lift generated by the wing as a function of the distance from the root y. Lr and Lt are the values of lift at the wing root and tip, respectively. (a) Derive the equations of motion for this 2 - DOF system and write them in a state space form. The equation should be in terms of the variables given in the figure. (b) The lift force at the tip of the wing is Lt not equal 0. Does this make sense? Why or why not? Winglet 0 WW C2 k L(v) b/2 L Combined Fuselage and wing mass J Moment of inertia of wing about point R | Mg = R k Figure 2: Idealized mechanical model of an airplane and wing. An airplane with a flexing wing in flight shown in the top sketch can be idealized by the mechanical model shown in the bottom sketch. L(y) is the lift generated by the wing as a function of the distance from the root y. Lr and Lt are the values of lift at the wing root and tip, respectively. (a) Derive the equations of motion for this 2 - DOF system and write them in a state space form. The equation should be in terms of the variables given in the figure. (b) The lift force at the tip of the wing is Lt not equal 0. Does this make sense? Why or why not? Winglet 0 WW C2 k L(v) b/2 L Combined Fuselage and wing mass J Moment of inertia of wing about point R | Mg = R k Figure 2: Idealized mechanical model of an airplane and wing.