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‫Welcome back.

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‫Let's now apply our rotation matrix using the convention are sub Z, Y and X, so small letters.

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‫So we are using the oilor angle approach.

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‫We are rotating about the moving body frames for Z, then Y and then X..

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‫Now, when we measure velocities of a drone, we typically do it in the body frame, not in the inertia

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‫frame.

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‫The velocities in the inertia frame would be something like this big X dot, the time derivative, big

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‫Y dot and big Z dot and all of them would be in meters per second.

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‫However, the last is in the body frame would be something like this small X dot here, small Y dot

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‫here and small Z dot here.

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‫And in this course we will call them like this.

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‫This will be small you this will be small V and this will be small w now remember these are linear velocities

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‫in the body frame, so their units are meters per second.

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‫We also had body frame angular velocities that we called P, Q and R and these were angular velocities.

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‫So their units where radians per second.

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‫All right, so don't confuse them.

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‫Linear velocities in the body frame make the drone translate in the direction of the body frame axis,

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‫meaning that the origin of the body frame actually moves with respect to the inertia frame.

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‫So the drone moves from one point in space to another point in space.

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‫And in case of angular velocities, the origin of the body frame stays in the same place.

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‫But the drone simply rotates about the body frame X, Y and Z axis.

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‫And of course, when your drone moves, then it will experience both linear and angular velocities.

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‫Now we have the body frame, linear velocities, but in order to control the drone, we also need to

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‫have the initial frame, linear velocities.

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‫And so the task of the rotation matrix is to convert the velocities in the body frame into the inertial

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‫frame.

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‫It's exactly the same thing that we did when we worked with a car in 2D.

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‫Only now we're working in 3D.

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‫So we have one more linear velocity in the inertial frame, big Z dot and one more linear velocity in

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‫the body frame.

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‫Small WSDOT and remember, the motion of the OV is the same.

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‫It's just we are representing the velocity of the drone in different ways.

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‫First, we represent the velocity of the drone in the body frame and then using the rotation matrices,

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‫we obtain the velocity of the drone represented in the initial frame because we need it for the controller.