Geometric Methods for Efficient Planar Swimming of Copepod Nauplii

Copepod nauplii are larval crustaceans with important ecological functions. Due to their small size, they experience an environment of low Reynolds number within aquatic habitat. Here we provide a mathematical model swimming copepod nauplius two legs moving in plane. This allows for both rotation and two-dimensional displacement by the periodic deformation swimmer’s body. The system is studied from framework optimal control theory, simple cost function designed approximate mechanical energy expended copepod. We find that this sufficiently realistic recreate behavior similar those observed nauplii, yet much analysis tractable. In particular, show controllable, but there exist singular configurations where degree non-holonomy non-generic. also partially characterize abnormal extremals explicit examples families curves. Finally, numerically simulate normal observe some interesting surprising phenomena.