Linear induction motors are under development for a variety of demanding applications including aircraft launchers and magnetically levitating trains. These applications require machines that can produce large forces, operate at high speeds, and can be controlled precisely to meet performance requirements. The design and implementation of these systems require fast and accurate techniques for performing system simulation and control system design. We present techniques for modeling and controlling linear induction machines based on a direct and quadrature (DQ) representation of the system dynamics. Simulation results using the DQ representation of the machine dynamics are presented and compared to test data from a Subscale Integration Test Bed developed for the U.S. Navy's Electromagnetic Aircraft Launch System program.