Quaternions and spatial rotation of a circle representing a particular rotation angle will be half of the angle represented by that rotation, since as the point is moved from the north to south pole, the latitude ranges from zero to 180 degrees, while the angle of rotation ranges from 0 to 360 degrees. (the "longitude" of a point then represents a particular axis of rotation.) Note however that this set of rotations is not closed under composition. Two successive rotations with axes in the "xy" plane will not necessarily give a rotation whose axis lies in the "xy" plane, and thus cannot be represented
Degrees of freedom (mechanics) rotation, which means that it has six degrees of freedom. The exact constraint mechanical design method manages the degrees of freedom to neither underconstrain nor overconstrain a device. The position of an "n"-dimensional rigid body is defined by the rigid transformation, ["T"] = ["A", "d"], where "d" is an "n"-dimensional translation and "A" is an "n" × "n" rotation matrix, which has "n" translational degrees of freedom and "n"("n" − 1)/2 rotational degrees of freedom. The number of rotational degrees of freedom comes from the dimension of the rotation group SO(n). A non-rigid or deformable body may be thought of