Can a Rigid Body's Rotation Be Described with Only Two Successive Rotations?

[Barkan]

I try to clearify it as much as I can, and I greatly appreciate the given answers.

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.

 

[bluelava0207]

So you only have yaw and pitch, but no roll. Camera tripods rotate this way. You can point the camera in ANY direction, so you're not limited there. However, you cannot point the camera at an object and then roll the camera to take an upside-down picture for example. That's what you lose by only having two rotations.

If this doesn't help any, do you think you can clarify the question? What is the motivation (what exactly are you trying to do?)

 

[bluelava0207]

I made a small mistake in my previous post. You could actually take a picture in any direction upside-down. You would do this by yawing so that you're pointing in the opposite direction, then pitching the camera so that it's inverted to look at the object.

So 0 degrees and 180 degrees are special cases. In general, you cannot take a rotated picture of an object.