‫Welcome back and here's your answer when you decompose the longitudinal velocity vector and the lateral
‫velocity vector, then it will become apparent how the answer is found.
‫We're going to shift the body frame here to match the origins of the body frame and the inertial frame.
‫And remember, we can shift the body frame around as we please, because when we deal with orientation,
‫then we don't care about the position of the body frame with respect to the initial frame.
‫We only care about the angles, how the body frame is oriented with respect to the inertial frame.
‫And so when we shift our body frame, for example, to this place, then the angle here is the same,
‫like the angle here.
‫And that's why you can shift the body frame around as you want, because the angles are the same, the
‫angles don't change.
‫And you can see that the inertia frame accident is formed by the positive X component of the longitudinal
‫velocity and by the negative X component of the lateral velocity.
‫That is why the value in front of Y dot here is negative.
‫However, the inertia frame y dot is composed of the positive y component of the longitudinal velocity
‫and also a positive y component of the lateral velocity.
‫Both components point up.
‫OK, so we have represented the big X dot and the big Y dot in terms of small X dot, small Y dot and
‫the Passi angle.
‫In other words, we have represented the velocities that were initially in the body frame.
‫We have represented them in the inertial frame.
‫But now another thought exercise for you.
‫Can you think of another way how to represent this relationship?
‫Can you take this relationship and simply reformulated?
‫The relationship will be the same.
‫Tried to put it in a different form and you will see the solution in the next video.
‫Thank you very much.
‫And see you there.