Mechanical face seals are constitutive components of turbomachines, which in turn can be constitutive to other systems (e.g. aircraft). Furthermore, the rotating element of a face seal is inextricably coupled to the turbomachine via a flexible mount, and the stationary seal element is coupled to the rotating seal element via the fluid film existing between the seal faces. Consequentially, understanding interactions between the seal and turbomachine is important for quantifying seal performance and improving its design. With few exceptions, previous works study the face seal dynamics independent from the rotordynamics. In addition, most prior investigations consider only angular and axial seal dynamics and neglect eccentric (i.e. lateral) deflections of the seal element(s). For the first time, this work develops a comprehensive and novel model of a mechanical face seal in the inertial reference frame including coupled rotordynamics and inertial maneuver loads of the overall system. The model is developed for a general seal geometry where both seal elements, stationary and rotating, are flexibly mounted and allowed to undergo angular, axial, and eccentric deflections. In addition, the seal model presented here accounts for transient operation, fluid shear forces, seal face contact, friction, and thermoelastic deformation. Finally, various faults due to manufacturing imperfections, component flaws, and/or installation errors can be accounted for by incorporating static angular misalignment of both seal elements, dynamic angular misalignment of the rotating seal element, eccentric rotating imbalance, and axial offset of the rotating seal element center of mass. Throughout this work, the equations of motion developed are valid for both steady-state and transient operation. This comprehensive model significantly advances the state of the art in mechanical face seal dynamic modeling and represents a pivotal step towards analyzing seal performance regarding a broad diversity of realistic problems.