Movement of passenger crews in a rarefied air tube at speeds over 600 km/h involves the effect of magnetic levitation and a traction linear superconducting synchronous motor with a stator winding distributed along the length of the tube and a superconducting excitation system on the crew. Conditions of magnetic levitation stipulate that the position of the crew in the tube is characterized by six degrees of freedom, so a traction linear superconducting synchronous motor must be considered as a multi-stage dynamic system. However, in the “normal” operational mode, the problem is reduced to consideration of the system with one degree of freedom with the coordinate that determines the position of an inductor with superconducting winding and without ferromagnetic cores relative to the running magnetic field of the stator winding. The specifics of magnetic levitation of the moving crew, which consists in the possibility of its spatial displacement, cause the appearance of geometric parameters characterizing progressive and rotational perturbations of the coordinates of the center of inertia of the crew in expressions for mutual inductances between the superconducting excitation system, electromagnetic shield, and the stator phase windings.