MAE142_Solution2

# MAE142_Solution2 - MAE 142 Homework Set#2(Winter 2011...

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MAE 142 Homework Set #2 (Winter 2011) Problem 1 Find the constant course heading that is needed to plan a two- hour airplane trip from Washington Dulles airport (IAD) to Orlando Florida airport (MCO). Assume a constant 30 nmi/hr wind that is moving in a direction pointed 60 deg east of true north. Problem 2 The gravity vector has a magnitude 'g' and points in the 'down' direction of a NED local frame. Use the Euler angle formulation of the L2B transformation matrix to find an expression for the gravity vector in body-fixed coordinates. Problem 3 Find the quaternions that result in the following B2L transformation matrix. T B2L = [ 0.66 0.49 0.56 0.66 0.73 0.14 0.34 0.47 0.81 ] Problem 4 Estimate and plot the Euler angle time histories using the rate gyro data provided on the class website. Numerically integrate the angular rate differential equations using both the Euler and quaternion formulations. Assume the Euler angles are initially set to zero.

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