Abstract-
We are interested in the locomotion of aquatic animals due to the coupling
between their shape changes and the surrounding fluid dynamics. In this talk,
we present a hierarchy of models for describing fishlike swimming in a perfect
fluid. The models rely on tools from geometric mechanics similar to those
used in studying the falling cat problem where the cat reorients itself by 180
degrees by merely changing its shape. The same approach can be applied to
analyze the dynamics of a new skateboard design called the Wave\texttrademark.
Indeed, the geometric framework is especially well suited for this class of
locomotion problems, that is, locomotion due to shape changes, because the net
locomotion is expressed in terms of the shape variables. Further, this
approach allows us to address the problem of motion planning or trajectory
design as one in optimal control; that is, we seek the most efficient shape
changes that achieve a desired net locomotion.
For illustration purposes, we
show examples of a two-dimensional articulated body propelling and steering
itself due to shape changes only. We conclude by discussing the extension of
these models to the interaction of the fish with point vortices and other
future directions.
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