Analytical Lagrangian model for constrained multi-body systems subjected to Froude-Krylov forces

Hybrid wind-wave systems are an active research topic with the goal of utilizing WECs in the solution of the challenging problems of deep-sea floating wind applications. A challenge arises as the modeling of these complex multi-body structures in ocean conditions usually rely on sophisticated numerical frameworks, which complicate the development of control or co-design research given the lack of analytical models. With the long-term goal of creating an analytical model for an OC3 + point absorber hybrid platform, this paper presents an initial development of an analytical Lagrangian approach to model multi-body constrained system subjected to Froude-Krylov forces. The justification to modeling considering only a Froude-Krylov approximation is discussed on the introduction, followed by a step-by-step description of the proposed modeling methodology. This model approach is then used in a case study to illustrate some of the possible analysis and results it is capable of obtaining. Although validation with other numerical frameworks were not yet used to compare results at this stage in the research, consistency checks were used to initially verify the intuitive dynamics behavior of the system and eliminate the risk of critical errors on the model. Further results and analysis are shown for the dynamics of motion and power for the case study system. The development of this analytical tool may aid in future works, such as hybrid system structure co-design and control implementations.