> But in the pitch = 90 degrees case I cannot easily understand how can > I think the roll. When the pitch attitude is 90 degrees nose-up or nose-down, the yaw attitude (heading) and roll attitude (bank angle) become undefined. (I've now found that this was also pointed out in this related answer which also has some other content that pertains to your question: https://aviation.stackexchange.com/questions/16531/what-is-the-relation-between-roll-angle-and-pitch-angle/16538#16538 : ) > **This describes almost every possible attitude uniquely, unless the pitch angle is +/- 90 degrees. Then roll and yaw will become > ambiguous.** Note that if you are banked (i.e. nonzero bank attitude or roll attitude, which ever you prefer to call it), then a motion that purely involves a nose-up pitch rotation and no yaw rotation or roll rotation will also increase the bank angle, and will also change the heading. Note also that a constant-banked climbing or descending turn (i.e. nose-up or nose-down pitch attitude) at a constant pitch attitude involves a roll rotation as well as pitch and yaw rotations. So, a pitch rotation is not exactly the same as a change in pitch attitude...and a lack of roll rotation does not always imply that the bank attitude (roll attitude) is not changing-- it's all a little complicated isn't it. The rate of rotation about any given axis (pitch, yaw, or roll) is not the same as the rate of change of the pitch attitude, yaw attitude (heading), or roll attitude (bank angle), respectively. For example an aircraft pointing straight up can YAW through 180 degrees and end up pointing straight down-- it has changed pitch attitude with no pitch rotation. > Update to the question: I wonder whether any (yaw, pitch, roll) triple > set exactly describes the attitude/orientation of an aircraft or not. > So could you please tell me that can any orientation of a flying > object described with a unique y,p,r triplet? In ALMOST all cases the answer is "yes". The exception is when the nose is pointing straight up or straight down (i.e. the pitch attitude is plus or minus 90 degrees). In that case the yaw and roll attitude (heading and bank angle) become undefined and there is no way to distinguish between the belly pointing north, south, east, or west. It has been noted that this can be resolved through the use of "quaternions". To learn more about that, you should probably ask another question.