Modeling floating bodies in shallow water

We study the motion of a floating rigid body in shallow waters using the Lagrangian formalism and Hamilton’s principle. For simplicity, the rigid body is assumed to be constrained to move only in the vertical direction and the boundary of the rigid body which is in contact with the fluid, the so-called wetted surface c w , is assumed to be the graph of a function. Equations of motion are derived in this way for a general function c w and later applied to the particular case when c w is given by a parabola centered at the origin.