hi guys,
To describe the position and orientation of a rigid body in a world coordinate system, we usually attach a coordinate system to the body and then give a description of this coordinate system relative to the world coordinate system. One way to describe the body-attached coordinate system is write three orthonormal vectors of its three principal axes in terms of the world coordinate system. It will be convenient if we stack these three vectors together as the column of a 3X3 matrix, we call this matrix a rotation matrix, but what's the order of the three vectors? Different orders will have different results? The determinant of the rotation matrix may be -1, that is an improper rotation matrix, but it can represent the orientation of the rigid body. So how to determine the order of the three vectors in the rotation matrix? Anyone can clarify it? thank you! 
