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 &times; n rotation matrix, which has n translational degrees of freedom and n(n − 1)/2 rotational degrees of freedom.
A non-rigid or deformable body may be thought of as a collection of many minute particles (infinite number of DOFs), this is often approximated by a finite DOF system.