1- Consider an aircraft flying due east along the equator. Define an Earth-fixed coordinate system F_(E) at zero longitude and zero latitude, and a local horizontal coordinate system F_(H) fixed to the center-of-gravity (CG) of the aircraft.Describe the relationship between the axes of f FE and F_(E) F_(H) at the instant the aircraft is at zero longitude and zero latitude, and again at the instant it is at 180 deg east longitude and zero latitude. 2 -An airplane is in a spin with constant phi =-50^circ and constant Theta =-50^circ See Figures 4.2 and 4.3 in your textbook. The rotation rate is constant as well, psi =30deg/s . At time t=0 the aircraft passes through due north, phi =0. Define the orientation of the body axes relative to F_(H) at this instant as F_(1) The aircraft continues to rotate about an axis pointed toward the ground . Six seconds later the body axes are oriented differently;define this orientation as F_(2)

1- The Earth-fixed coordinate system $F_{E}$ is a global coordinate system that is fixed to the Earth's surface. It is defined by the zero longitude and zero latitude, which correspond to the prime meridian and the equator, respectively. The local horizontal coordinate system $F_{H}$ is a coordinate system that is fixed to the center-of-gravity (CG) of the aircraft. It is defined by the horizontal axes that are perpendicular to the aircraft's flight path.<br /><br />At the instant the aircraft is at zero longitude and zero latitude, the axes of $F_{E}$ and $F_{H}$ are aligned with each other. This means that the north-south axis of $F_{E}$ is parallel to the north-south axis of $F_{H}$, and the east-west axis of $F_{E}$ is parallel to the east-west axis of $F_{H}$.<br /><br />At the instant the aircraft is at 180 deg east longitude and zero latitude, the axes of $F_{E}$ and $F_{H}$ are no longer aligned. This is because the aircraft has moved 180 degrees eastward, which means that the north-south axis of $F_{E}$ is now pointing towards the south, while the north-south axis of $F_{H}$ is still pointing towards the north. Similarly, the east-west axis of $F_{E}$ is now pointing towards the west, while the east-west axis of $F_{H}$ is still pointing towards the east.<br /><br />2- At time $t=0$, the aircraft is passing through due north, which means that the $\phi$ angle is 0 degrees. At this instant, the orientation of the body axes relative to $F_{H}$ is defined as $F_{1}$. The $\Theta$ angle is also 0 degrees, which means that the body axes are aligned with the horizontal axis of $F_{H}$.<br /><br />Six seconds later, the body axes are oriented differently. This is because the aircraft has been rotating about an axis pointed toward the ground, which means that the $\phi$ angle has changed. The new orientation of the body axes is defined as $F_{2}$. The $\Theta$ angle has also changed, which means that the body axes are no longer aligned with the horizontal axis of $F_{H}$.