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Question 1 (10p) The aircraft equations of motion are derived from Newton’s second law using the body axis system and are then transformed to an inertial axis system. This axis transformation of an arbitrary time derivative vector can be written as: dA/dt | INERTIAL = dA/dt | BODY + ? × A The aircraft center of gravity velocity vector is vC = ui + vj + wk. The rotational velocity vector ? = pi + qj + rk indicates the total angular rate of the aircraft within the body axis system. The i, j and k are the unit vectors along the x, y and z axis respectively. a. State the meaning of the angular rates p, q and r. b. Calculate the velocity ? × vC using the given vector notations for the linear velocity vector and the angular velocity vector. c. Determine the acceleration vector of the center of gravity of the aircraft in the inertial axis system. Solutions of the fundamental aircraft equations of motion can only be found numerically. For analytical solutions the equations are linearized by means of small perturbation theory. This means that some variables are replaced by an equilibrium value plus a small disturbance from the equilibrium state. For the lift we assume in this case: L = L0 + ?L. The expression for the aerodynamic lift is L = 1/2?U^2SCL. Assume that the lift coefficient is a constant. d. Find linearized expressions for L0 and ?L. (Tip: products of small disturbances vanish!)

          Question 1 (10p)
The aircraft equations of motion are derived from Newton’s second law using the body axis system and are then transformed to an inertial axis system. This axis transformation of an arbitrary time derivative vector can be written as:

dA/dt | INERTIAL = dA/dt | BODY + ? × A

The aircraft center of gravity velocity vector is vC = ui + vj + wk. The rotational velocity vector ? = pi + qj + rk indicates the total angular rate of the aircraft within the body axis system. The i, j and k are the unit vectors along the x, y and z axis respectively.

a. State the meaning of the angular rates p, q and r.
b. Calculate the velocity ? × vC using the given vector notations for the linear velocity vector and the angular velocity vector.
c. Determine the acceleration vector of the center of gravity of the aircraft in the inertial axis system.

Solutions of the fundamental aircraft equations of motion can only be found numerically. For analytical solutions the equations are linearized by means of small perturbation theory. This means that some variables are replaced by an equilibrium value plus a small disturbance from the equilibrium state. For the lift we assume in this case: L = L0 + ?L. The expression for the aerodynamic lift is L = 1/2?U^2SCL. Assume that the lift coefficient is a constant.

d. Find linearized expressions for L0 and ?L. (Tip: products of small disturbances vanish!)

Question 1 (10p)
The aircraft equations of motion are derived from Newton’s second law using the body axis system and are then transformed to an inertial axis system. This axis transformation of an arbitrary time derivative vector can be written as:

dA/dt | INERTIAL = dA/dt | BODY + ? × A

The aircraft center of gravity velocity vector is vC = ui + vj + wk. The rotational velocity vector ? = pi + qj + rk indicates the total angular rate of the aircraft within the body axis system. The i, j and k are the unit vectors along the x, y and z axis respectively.

a. State the meaning of the angular rates p, q and r.
b. Calculate the velocity ? × vC using the given vector notations for the linear velocity vector and the angular velocity vector.
c. Determine the acceleration vector of the center of gravity of the aircraft in the inertial axis system.

Solutions of the fundamental aircraft equations of motion can only be found numerically. For analytical solutions the equations are linearized by means of small perturbation theory. This means that some variables are replaced by an equilibrium value plus a small disturbance from the equilibrium state. For the lift we assume in this case: L = L0 + ?L. The expression for the aerodynamic lift is L = 1/2?U^2SCL. Assume that the lift coefficient is a constant.

d. Find linearized expressions for L0 and ?L. (Tip: products of small disturbances vanish!)

Added by Daniel M.

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