  We examine the stability of the "coast" motion of fish, that is to say, the
motion of a neutrally buoyant fish at constant speed in a straight line. The
forces and moments acting on the fish body are thus perfectly balanced. The
fish motion is said to be unstable if a perturbation in the conditions
surrounding the fish results in forces and moments that tend to increase the
perturbation and it is stable if these emerging forces tend to reduce the
perturbation and return the fish to its original state. Stability may be
achieved actively or passively. Active stabilization requires neurological
control that activates musculo-skeletal components to compensate for the
external perturbations acting against stability. Passive stabilization on the
other hand requires no energy input by the fish and is dependent upon the fish
morphology, i.e. geometry and elastic properties. In this paper, we use a
deformable body consisting of an articulated body equipped with torsional
springs at its hinge joints and submerged in an unbounded perfect fluid as a
simple model to study passive stability as a function of the body geometry and
spring stiffness. We show that for given body dimensions, the spring
elasticity, when properly chosen, leads to passive stabilization of the
(otherwise unstable) coast motion.
