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In this paper, we develop an illustrative, physically unified model for treating a solenoidal reluctance linear accelerator. A simplified field-based physical model is developed from basic principles and cast in a variational (Lagrangian) form. The equations of motion are presented in a convenient form for computation, from which a fast and compact numerical model is constructed that also accounts for the effects of core saturation as well as the energy exchange between the field and armature motion. The results of this model are then compared with experimental results obtained from a small-scale mass launcher apparatus. Good agreement between experimental and computed behavior has been observed.