The basic model used for a snake is the sol called slender elastic body model (the cosserat model). Visualised below
This model uses the differential geometry of frames to derive a system of partial differential equations which combine the internal mechanics (musculature) of the body and its external interaction (friction) to model its motion. It has been used to model DNA, spermatozoa, space cables, proteins, growing plants, the optic nerve and sea-shell growth amongst other
It can also be used to model tentacle and antennae whipping, in this case the shape of the filament matters a lot for the allowed range of motion and most efficient whipping shape. The image below is of an octopus filament model by Alex Rowan-Smith whose 4th year project is in the links at the bottom of the page (have a look at this for an animated version, and others)
The student will investigate some aspect of snake or tentacle motion (or something similar if another interesting biological motion is found) . A significant focus will be on the effect of adding a more sophisticated friction/viscousity model on the range of possible dynamics. In practice this will involved some analytic work and some numerical work (the exact balance can be chosen by the student as the project proceeds). The numerical work can be performed in Python, Julia, C++ or Java. I cannot stress enough that you do not need to be an experienced coder to perform this task. I have have many students tell me they are not confident with coding over the years, only to go ahead and create excellent projects which involve solving P.D.E's numerically.
If you have any questions please contact me via email. I am happy to give your more details.
None, even with a numerical approach my experience has been that students can develop sufficient skills during the project to treat complex systems. However, any of the following modules could be helpful: Mathematical Biology III, Differential geometry or fluid mechanics or Partial Differential Equations III/IV. It would match very well with the 4th year mathematical biology course!!
email: Chris Prior