Hamilton's principle for a hydromagnetic fluid with a free boundary

Newcomb's non-linear formulation of Hamilton's principle for an ideal hydromagnetic fluid surrounded by a wall is generalized to allow vacuum and ferromagnetic regions, and to include the effects of external conductors and circuits. The linear approximation is recovered by expanding to second order in the plasma displacement. When the accumulated charge flowing in each conductor is treated as a generalized variable, the vacuum energy appears as a kinetic energy, with the inductance matrix playing the role of a mass tensor. As an application, the generalization of the Luest-Martenson form of deltaW is found for the case of passive feedback due to interconnection of the external coils. A subsidiary variational principle is used to determine the inductance matrix, thus providing an alternative to the Green's function method. (author)