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Published August 2005 | public
Journal Article

Locomotion of Articulated Bodies in a Perfect Fluid


This paper is concerned with modeling the dynamics of N articulated solid bodies submerged in an ideal fluid. The model is used to analyze the locomotion of aquatic animals due to the coupling between their shape changes and the fluid dynamics in their environment. The equations of motion are obtained by making use of a two-stage reduction process which leads to significant mathematical and computational simplifications. The first reduction exploits particle relabeling symmetry: that is, the symmetry associated with the conservation of circulation for ideal, incompressible fluids. As a result, the equations of motion for the submerged solid bodies can be formulated without explicitly incorporating the fluid variables. This reduction by the fluid variables is a key difference with earlier methods, and it is appropriate since one is mainly interested in the location of the bodies, not the fluid particles. The second reduction is associated with the invariance of the dynamics under superimposed rigid motions. This invariance corresponds to the conservation of total momentum of the solid-fluid system. Due to this symmetry, the net locomotion of the solid system is realized as the sum of geometric and dynamic phases over the shape space consisting of allowable relative motions, or deformations, of the solids. In particular, reconstruction equations that govern the net locomotion at zero momentum, that is, the geometric phases, are obtained. As an illustrative example, a planar three-link mechanism is shown to propel and steer itself at zero momentum by periodically changing its shape. Two solutions are presented: one corresponds to a hydrodynamically decoupled mechanism and one is based on accurately computing the added inertias using a boundary element method. The hydrodynamically decoupled model produces smaller net motion than the more accurate model, indicating that it is important to consider the hydrodynamic interaction of the links.

Additional Information

© 2005 Springer Science+Business Media, Inc. Received June 20, 2004; revised March 7, 2005; revision accepted April 9, 2005. Online publication August 5, 2005. Communicated by P. K. Newton. This research was partially supported by NSF-ITR grant ACI-0204932 and ONR Contract N00014-02-1-0826.We are grateful to Joel Burdick, Scott Kelly, Jim Radford, and Banavara Shashikanth for their useful comments and inspiration over the years.

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August 19, 2023
October 20, 2023