Stability of a Bottom-Heavy Underwater Vehicle
In Automatica, Volume 33, Number 3, March 1997, p. 331-346.
In this paper we study stability of underwater vehicle
dynamics for a six degree-of-freedom vehicle modelled as a
neutrally buoyant, submerged
rigid body in an ideal fluid.
We consider the case in which the center of gravity and the center of buoyancy
of the vehicle are noncoincident such that
gravity introduces an orientation-dependent moment. Noting that
Kirchhoff's equations of motion for a submerged
are Hamiltonian with respect to a Lie-Poisson structure,
we derive the Lie-Poisson structure for the
underwater vehicle dynamics with noncoincident
centers of gravity and buoyancy.
Using the energy-Casimir method we then derive conditions for nonlinear
of relative equilibria, i.e., stability of motions corresponding to
constant translations and rotations. The conditions reveal
for the vehicle stability problem the relevant design parameters, which
in some cases can be interpreted as control parameters.
Further, the formulation provides a setting
for exploring the stabilizing and destabilizing effects of dissipation
and externally applied control forces and torques.
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