The U.S. Bureau of Mines is conducting an ongoing research project to better understand the phenomena involved within electric arcs utilized in electric furnace steelmaking. With a better understanding of the physical and electrical characteristics involved, dynamic or predictive control of electric arc furnaces may be possible. A mathematical model is presented, but not solved, and the system of coupled equations is analyzed. Characteristic parameters are used to determine relative importance. In this manner, significant quantities are defined. The parameters found to contribute little to the system of equations of motion are ignored. A resultant simplified system is identified, and directions for further study are indicated toward control of electric arc furnaces.