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‫Welcome back.

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‫And now we're going to start discussing rotation matrices.

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‫So how would we describe the attitude of the drone in space?

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‫Well, again, you compare the inertia frame with the body frame.

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‫However, this time, you don't compare the distances of their origins between them.

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‫You compare how the body frame is rotated with respect to the inertia frame.

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‫And you measured that with Phi Theta and Passi Angles or Roll Pitch and your angles and the unit is

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‫Radiance.

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‫Now, let's make one thing clear first.

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‫When we talk about describing the attitude of the drone, it does not matter what the body frames position

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‫is with respect to the inertia frame.

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‫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

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‫frame X, Y and Z axes point exactly in the same direction, like the body frame X, Y and Z axis,

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‫the attitude of the drone is perfectly aligned with the inertial frame, meaning that Phi Theta and

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‫PSI equal zero radians.

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‫All right.

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‫And you can check that by simply shifting the body frame and putting it on top of the inertia frame

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‫like here, the body frame, X, Y, Z axis should perfectly overlap the inertial X, Y and Z axis when

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‫you join their origins.

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‫But now let's start changing the body frame attitude with respect to the inertia frame.

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‫Let's for a second forget about 3D and focus on a 2D case.

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‫If you remember in the previous course in the series, we had a car on a two day plane.

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‫We had an inertial reference frame, X and Y, and also a body frame, small X and small Y.

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‫The body frame formed a BPCI angle with respect to the initial frame.

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‫You can also say that the body frame was rotated with respect to the inertia frame by BPCI irradiance

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‫counterclockwise.

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‫The car had a longitudinal velocity, small x dot which was in the body frame X direction and lateral

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‫velocity, small Y dot in the body frame Y direction.

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‫These velocities were represented in the body frame, but we wanted to represent them in the inertial

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‫frame.

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‫In other words, we wanted to know what big X dot and big Y that were.

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‫So here's a revision exercise for you.

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‫Try to fill in the gaps by yourself and you will see the solution in the next video.

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‫How would you represent the inertial X and Y dot in terms of body frame X and Y dot and the Passi angle?

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‫See you in the next video.