Large offshore renewable energy investments require the use of maintenance boats to keep them in operable conditions. Unfortunately, due to rough seas in some of the project locations, the transferring of crew members from vessel to turbine or platform is no easy task. Thus, the research presented is focused at further looking into add on stability systems for marine vessels to further ease the process of offshore platform maintenance and crew member safety. The rolling and pitching of ships and boats induced by the ocean waves results in undesirable motion. In an effort to increase the stability of the deck/platform and human comfort and safety, various add-on stability systems have been developed. Of interest in the research presented are internal active systems, specifically the active gyroscopic stabilizer. Previous research and industrial use of active gyroscopic roll stabilizers has shown and proven the effectiveness of the system to reduce rolling motion. The research presented here is focused on developing a more detailed mathematical analysis of a marine vessel installed with active gyroscopic roll stabilizer(s). Through the use of the moving frame method developed by the second author, a novel approach has been developed to derive a mathematical model for two different cases: 1) a marine vessel with a single gyroscopic roll stabilizer and 2) a marine vessel with two gyroscopic roll stabilizers. The moving frame method allows for a systematic derivation despite the increase in complexity of the system as the number of stabilizers is increased. Lastly, the nonlinear equations of motion of a ship with a gyroscopic roll stabilizer are derived.