The Hydrodynamics of Ammonoid Swimming: Equations of Motion and Rocking Resonances

This work explores the swimming of ammonoids, cephalopods related to living squids, octopuses, and nautilids and, like the latter, equipped with a coiled external shell. A mathematical model is introduced for theoretical ammonoid conchs. The two differential equations of motion (one for the centre of mass, including the drag force and the added mass coefficient, and one for the roll angle) are solved numerically for the theoretical conchs, and the results are analysed in terms of velocity and rocking angle. Destabilising resonances occur when the rocking motion is in phase with the propelling water jet. It is suggested that the ammonoids partly evolved avoiding the occurrence of such resonances in their construction.