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In this study, hydrodynamic forces on a submerged vessel maneuvering near a free surface are determined using a reformulated Lagrangian nonlinear maneuvering and seakeeping model derived using Lagrangian mechanics under ideal flow assumptions. A Lagrangian mechanics maneuvering model is first reformulated to simplify the computation of parameters; then, incident wave effects are incorporated into the reformulation; finally, the parameters are computed using a medium-fidelity time-domain potential-flow panel code. Predictions from the reformulated Lagrangian nonlinear maneuvering and seakeeping model, whose parameters are computed using the methods described here, are compared with direct numerical computations in two steps for a prolate spheroid maneuvering in the longitudinal plane near the free surface. First, the hydrodynamic force and moment predicted by the model are compared with solutions from the panel code for sinusoidal motion in surge, heave, and pitch in calm water. Second, the hydrodynamic force and moment are investigated for cases where the spheroid maneuvers to approach the surface in calm water and in plane progressive waves. To conclude, a physically intuitive formulation of the Lagrangian nonlinear maneuvering and seakeeping model is presented for control applications and simulations.

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