This paper presents new method in dynamics — the Moving Frame Method (MFM) — and uses it to address a challenge faceing Norwegian shipping. Large offshore renewable energy investments require the use of maintenance boats to keep them in operable conditions. Unfortunately, due to rough seas in some project locations, the transferring of crew members from vessel to turbine or platform is fraught with safety concerns. These concerns can be alleviated by controlling the motion of the transfer vessel. This research studies an add-on stability system for marine vessels to ease the process of offshore platform maintenance and crew member safety. Specifically, this research concerns an internal active system — an active gyroscopic stabilizer — and a more powerful method of theoretical and computational mechanics. This paper derives the equations of motion of a model system equipped with dual gyroscopic stabilizers, using the MFM. The equations of motion are numerically solved to obtain a numerical simulation. The method exploits a variational principle with a restricted variation of the angular velocity. The MFM simplifies dynamics, enables a consistent notation, from 2D to 3D analysis and exploits matrix algebra in lieu of the vector cross product. Finally, in a companion paper to this one, the mathematical model and the numerical simulation is verified with experiments conducted in a large-scale wave tank.

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