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Suppose that we have a rigid body. We attach a movable coodinate frame on this body.

Normally, if I perform 3 successive rotations such as Z-Y-X or Z-Y-Z (or any other 24) I can describe its rotation in the most general case.

If I perform only two rotations what will happen then? Let's suppose I only perform a Z-Y rotations (first rotate about yaw then rotate about the current pitch) what would be the loss in terms of generality? Let's say, without the 3rd successive rotation, I cannot describe the half of the ... plane and/or sphere?

Thank you very much in advance.