A two winding machine is operated as a single phase synchronous generator. The round rotor is running with fixed speed and the rotor winding is?

A two winding machine is operated as a single phase synchronous generator. The round rotor is running with fixed speed and the rotor winding is running a constant D.C voltage source, the self-inductance of the tow winding are constant while the mutual inductance between them is a pare cosine function of the angle between their axis.     The stator winding is initially open when a sudden short-circuit ocours at its terminals.

Assume reasonable values for the parameters and supply and develop a program to solve the differential equation and calculate, numerically the short circuit current.