John: You are inventing your own terminology. Rotation is not the property of anything that can be rotated. Rotation is an action that can be performed upon anything that can be rotated. Hence, rotation can be used to describe the relative orientation of two coordinate systems, that is, it describes the action that must be applied to map one into the other. But the rotation mapping one into the other is a property of neither, but a property of the two of them relative to each other. Your sources say exactly this, and do not support your usage.