The set of coordinates that define the position of a reference point and the orientation of a coordinate frame attached to a rigid body in three-dimensional space form its configuration space, often denoted R 3 × × S O ( 3 ) where R 3 represents the coordinates of the origin of the frame attached to the body, and S O ( 3 ) represents the rotation matrices that define the orientation of this frame relative to a ground frame. A configuration of the rigid body is defined by six parameters, three from R 3 and three from S O ( 3 ) , and is said to have six degrees of freedom.