  The modified nodal analysis (MNA) is probably the most widely used
formulation for the modeling and simulation of electric circuits. Its
conventional form uses electric node potentials and currents across inductors
and voltage sources as unknowns, thus taking an electric viewpoint. In this
paper, we propose a magnetic oriented nodal analysis (MONA) for electric
circuits, which is based on magnetic node potentials and charges across
capacitors and voltage sources as the primary degrees of freedom, thus giving
direct access to these quantities. The resulting system has the structure of a
generalized gradient system which immediately ensures passivity in the absence
of sources. A complete index analysis is presented showing regularity of the
magnetic oriented formulation under standard topological conditions on the
network interconnection. In comparison to conventional MNA, the
differential-algebraic index is reduced by one in most cases which facilitates
the numerical solution. Some preliminary numerical experiments are presented
for illustration of the feasibility and stability of the new approach.
