Stability of a bottom-heavy underwater vehicle
The author studies the dynamics of an underwater vehicle modeled as a rigid body submerged in an ideal fluid. The vehicle is assumed to be neutrally buoyant, i.e., buoyant and gravitational forces are equal in magnitude and opposite in direction. In contrast to classical work of \textit{H. Lamb} [Hydrodynamics, (Cambridge Univ. Press, Cambridge) (1993; Zbl 0828.01012)] the gravitational and buoyant center of the body need not coincide. Viscuous effects are left out of the model. The dynamics are Hamiltonian with respect to a suitable Lie-Poisson structure. Equilibria in phase space correspond to constant (translation and/or rotational) motion of the vehicle. The author determines the equilibria and investigates their nonlinear (Lyapunov) stability behavior. Sufficient conditions for stability and instability are derived in terms of the equilibrium velocity and the system parameters such as masses and moments of inertia of the body fluid system and the distance between the centers of buoyancy and gravity. While the model is purely kinematic (does not involve controls) the author outlines how these stability conditions can be used to design control strategies that stabilize the vehicle motion.
scientific article; zbMATH DE number 1017012
scientific article