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This paper proposes the application of the Lagrange multiplier method to implement the relative motion of stator and rotor in the finite element (FE) simulations of electric machines. The nonconformity at the interface between stator and rotor regions imposes no restriction on time or space discretization. This freedom is highly valuable for domain decomposition. Through the choice of particular dual shape functions for the Lagrange multiplier, the symmetry, sparsity and positive definiteness of the linear system can be preserved. The method is applied to the 2-D simulation of a permanent magnet excited synchronous machine, and the results are compared with a conforming moving band approach with re-meshing of the air gap.