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The concept of d-q coupled circuits representing stator and rotor magnetic poles is widely used in the analysis of symmetrical round-rotor induction machines. In this paper conventional round-rotor theory is extended to the analysis of linear induction machines. In particular, a tenth order set of differential equations are derived which describe a basic model for a four pole machine. Higher order systems of equations are discussed which better incorporate leading and trailing end effects. The parameters used in the model are readily derived from classical round-rotor theory. The resulting model is inherently capable of simulating both steady-state and transient behavior.