GEOMETRICAL FORMULATION FOR VARIATIONAL ELECTROMAGNETICS

The choice of co-ordinates in the calculation of electromagnetic fields is difficult because the direction of the field varies from point to point. It is, therefore, desirable to use methods which are co-ordinate-free and are based on geometry rather than algebraic equations. Variational methods are particularly appropriate for systems dealing with geometrical objects having varying curvature. Such methods exist for mechanical systems and some of the results can be transferred to electromagnetics. It is shown that the geometrical approach to electromagnetics unifies the subject and that it gives guidance in the choice of simple numerical methods of calculation.