The hydromagnetic equations for an axisymmetric polytropic medium are transformed into six scalar equations. A partial solution of these equations is obtained for the case of equilibrium. A complete set of integrals of the axisymmetric hydromagnetic equations is given. It is shown that these integrals may be made the basis of a variational principle characterizing the states of equilibrium as states of extremal energy with respect to the set of integrals.
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L. Woltjer (1959) studied this question.