Generalization of the Kelvin-Kirchhoff equations for the motion of a body through a fluid

The classical Kelvin-Kirchhoff equations of motion of a rigid body in an inviscid, unbounded fluid are generalized for the case where other fixed boundaries are present. An interesting by-product of the derivation is a relation, new to the authors, between the direction cosines of the body axes relative to fixed axes and kinematic parameters of the angular motion of the body.