‫Welcome back.
‫Let's now apply our rotation matrix using the convention are sub Z, Y and X, so small letters.
‫So we are using the oilor angle approach.
‫We are rotating about the moving body frames for Z, then Y and then X..
‫Now, when we measure velocities of a drone, we typically do it in the body frame, not in the inertia
‫frame.
‫The velocities in the inertia frame would be something like this big X dot, the time derivative, big
‫Y dot and big Z dot and all of them would be in meters per second.
‫However, the last is in the body frame would be something like this small X dot here, small Y dot
‫here and small Z dot here.
‫And in this course we will call them like this.
‫This will be small you this will be small V and this will be small w now remember these are linear velocities
‫in the body frame, so their units are meters per second.
‫We also had body frame angular velocities that we called P, Q and R and these were angular velocities.
‫So their units where radians per second.
‫All right, so don't confuse them.
‫Linear velocities in the body frame make the drone translate in the direction of the body frame axis,
‫meaning that the origin of the body frame actually moves with respect to the inertia frame.
‫So the drone moves from one point in space to another point in space.
‫And in case of angular velocities, the origin of the body frame stays in the same place.
‫But the drone simply rotates about the body frame X, Y and Z axis.
‫And of course, when your drone moves, then it will experience both linear and angular velocities.
‫Now we have the body frame, linear velocities, but in order to control the drone, we also need to
‫have the initial frame, linear velocities.
‫And so the task of the rotation matrix is to convert the velocities in the body frame into the inertial
‫frame.
‫It's exactly the same thing that we did when we worked with a car in 2D.
‫Only now we're working in 3D.
‫So we have one more linear velocity in the inertial frame, big Z dot and one more linear velocity in
‫the body frame.
‫Small WSDOT and remember, the motion of the OV is the same.
‫It's just we are representing the velocity of the drone in different ways.
‫First, we represent the velocity of the drone in the body frame and then using the rotation matrices,
‫we obtain the velocity of the drone represented in the initial frame because we need it for the controller.