Dimensional-directional analysis by a quaternionic representation of physical quantities

The method of dimensional-directional analysis is established by a way which consists of the representation of the physical quantities as quaternions. Two dimensional-directional bases are obtained for the particular case of Newtonian mechanics. The dimensional-directional, the dimensional, the directional and the reduced-dimensional-directional equations are defined. Furthermore, the Principle of Dimensional-directional Homogeneity is established and the Buckingham π theorem is reformulated. Some examples show the powerfulness of the dimensional-directional analysis. Finally, the conversion matrices for a change of dimensional-directional basis are given.