Stability of a bottom-heavy underwater vehicle
type: Item
instance of: scholarly article
title: Stability of a bottom-heavy underwater vehicle
zbMATH Open document ID: 0872.93061
DOI: 10.1016/S0005-1098(96)00176-8
author: Naomi Ehrich Leonard
published in: Automatica
publication date: 1997-07-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 93B29
zbMATH DE Number: 1017012
zbMATH Keywords: underwater vehicle dynamics
zbMATH Keywords: rigid body model
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: energy-Casimir method
zbMATH Keywords: stabilization
reviewed by: Dirk Mittenhuber
MaRDI profile type: Publication
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full work available at URL: s0005-1098(96)00176-8
OpenAlex ID: W2093195174
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description: scientific article; zbMATH DE number 1017012