  We derive the non-linear dynamical equations for an augmented electromagnetic
railgun, whose augmentation circuit is inductively coupled to the gun circuit.
We solve these differential equations numerically using example parameter
values. We find a complicated interaction between the augmentation circuit, gun
circuit, and mechanical degrees of freedom, leading to a complicated
optimization problem. For certain values of parameters, we find that an
augmented electromagnetic railgun has an armature kinetic energy that is 42%
larger than the same railgun with no augmentation circuit. Optimizing the
parameters may lead to further increase in performance.
