1.

At t = 0, a launch vehicle takes off from the surface of the Earth at the equator with longitude L = 0. At t = 50 s, the vehicle has a longitude of 10 deg, latitude of 0, and an altitude of 50,000 ft. The velocity components measured with respect to the Earth-fixed ox _Ey _Ez _E system are u _E = 1500 ft/s, v _E = 3000 ft/s, and w _E = 0. Assuming that the Earth-fixed system ox _Ey _Ez _E coincides with the inertial system at t = 0, determine the position and velocity of the vehicle in the inertial reference system at t = 50 s.

2.

An aircraft is undergoing a steady rotation with angular velocity components in body axes system p = 10 deg/s, q = 2 deg/s, and r = 5 deg/s. At a certain instant of time, the Euler angles are ? = -30 deg, ? = 10 deg, and ? = 15 deg. Determine the corresponding Euler angle rates.

3.

An aircraft executes a velocity vector roll at an angle of attack of 40 deg with an angular velocity of 30 deg/s about the wind axis. Plot the time history of Euler angles for first 20 s.

4.

Using the method of direction cosines and quaternions, compute the time history of Euler angles for the aircraft in Example...