Abstract
It is seen in some natural biological situations, that a living organism requiring a change in its location and orientation is able to do so by executing a sequence of internally controlled motions. These motions cause a resultant location change due to the conservation of momentum. The first half of this study investigates various entities which have control of an internal configuration which when changed result in a change in external configuration; the 2-D diver, the falling cat, the astronaut and the falling gecko. The relationship between changes in the base space (internal configuration) and the location group (resultant external configuration) can be represented as a momentum-preserving connection on a principal fibre bundle. The second half of this study investigates the possibility of adapting a numerical panel method, used to model flow past an aircraft aerofoil, to the notion of a deformable 2-dimensional body submerged in an ideal, irrotational, quiescent fluid. The method is designed to model the movement of an amoeboid swimmer, such as the unicellular Synechoccocus genus, through a quiescent fluid. It is shown that the amoeba, which changes its surface shape, experiences a change in location within the fluid, including rotational and translational changes, due to the conservation of linear and angular momentum. We present a model for unicellular fluid transport using the connection associated with a panelled-surface approximation of the body. It is found that the model proposed was a reasonable, low-error, representation when compared with an analytical model for a particular type of small deformation. The model also caters for a wider range of deformations and extension to a higher-dimensional base space.