On principle of the least action in classical electrodynamics

The formulation of the electrodynamics principle of least action in case of description of interaction of some space-fixed bodies is given in this paper. The formulation is based on Poincare solution to this problem in electromagnetic theory. Minimization of action integral results in general Maxwell equations and corresponding boundary conditions. In addition, permissible transformations of Lagrange function allow to obtain any of six variants of Maxwell equations, where one of the following six pairs of field vectors E and H, E and B, D and H, D and B, D. and H, D. and B is used for description of electromagnetic processes and D. is solenoidal analog of vector D.