We describe basic considerations in the Lagrangian modeling of aquatic vehicles developing liftlike forces in a controlled way. We introduce the aquatic Flettner rotor as prototypical of this class of vehicles, and demonstrate the compatibility of Lagrangian formalism with experimental data describing a laboratory rotor. We analyze the controllability of a model for the rotor, connect its structure to that of models for Lagrangian systems subject to nonholonomic constraints, and present numerical evidence that our model can behave chaotically given physically motivated inputs and disturbances. We conclude with a description of a fishlike robotic vehicle employing a rotor in place of a caudal fin