The Inductrack system provides a novel way to achieve magnetic levitation by using Halbach arrays of permanent magnets (PMs). Due to the complexities of the nonlinear electro-magneto-mechanical coupling in the system, most previous analyses of the Inductrack system rely on steady-state results and consequently cannot fully capture the dynamic behaviors of the system in transient scenarios. In this article, a new three degrees-of-freedom (3DOF) transient model of the Inductrack system is proposed. This model describes the rigid-body motion of the Inductrack vehicle with axial (longitudinal) and vertical (transverse) displacements and pitch rotation, and it is derived without any assumption of steady-state quantities. Compared to a recently available 2DOF lumped-mass model developed by the authors, the inclusion of the pitch rotation in the new model results in a much more complicated mechanism of electro-magneto-mechanical coupling. Numerical results show that the pitch rotation can have a significant effect on the dynamic response and stability of the Inductrack system, which necessities vibration control for the safe operation of the Inductrack system.