‫Welcome back.
‫And now we're going to start discussing rotation matrices.
‫So how would we describe the attitude of the drone in space?
‫Well, again, you compare the inertia frame with the body frame.
‫However, this time, you don't compare the distances of their origins between them.
‫You compare how the body frame is rotated with respect to the inertia frame.
‫And you measured that with Phi Theta and Passi Angles or Roll Pitch and your angles and the unit is
‫Radiance.
‫Now, let's make one thing clear first.
‫When we talk about describing the attitude of the drone, it does not matter what the body frames position
‫is with respect to the inertia frame.
‫It can be here or it can be here, or it can be here or here or even here for as long as the inertia
‫frame X, Y and Z axes point exactly in the same direction, like the body frame X, Y and Z axis,
‫the attitude of the drone is perfectly aligned with the inertial frame, meaning that Phi Theta and
‫PSI equal zero radians.
‫All right.
‫And you can check that by simply shifting the body frame and putting it on top of the inertia frame
‫like here, the body frame, X, Y, Z axis should perfectly overlap the inertial X, Y and Z axis when
‫you join their origins.
‫But now let's start changing the body frame attitude with respect to the inertia frame.
‫Let's for a second forget about 3D and focus on a 2D case.
‫If you remember in the previous course in the series, we had a car on a two day plane.
‫We had an inertial reference frame, X and Y, and also a body frame, small X and small Y.
‫The body frame formed a BPCI angle with respect to the initial frame.
‫You can also say that the body frame was rotated with respect to the inertia frame by BPCI irradiance
‫counterclockwise.
‫The car had a longitudinal velocity, small x dot which was in the body frame X direction and lateral
‫velocity, small Y dot in the body frame Y direction.
‫These velocities were represented in the body frame, but we wanted to represent them in the inertial
‫frame.
‫In other words, we wanted to know what big X dot and big Y that were.
‫So here's a revision exercise for you.
‫Try to fill in the gaps by yourself and you will see the solution in the next video.
‫How would you represent the inertial X and Y dot in terms of body frame X and Y dot and the Passi angle?
‫See you in the next video.