Soft slender structures are ubiquitous in natural and artificial
systems, in active and passive settings and across scales, from
polymers and flagella, to snakes and space tethers. In this
paper, we demonstrate the use of a simple and practical
numerical implementation based on the Cosserat rod model to
simulate the dynamics of filaments that can bend, twist, stretch
and shear while interacting with complex environments via
muscular activity, surface contact, friction and hydrodynamics.
We validate our simulations by solving a number of forward
problems involving the mechanics of passive filaments and
comparing them with known analytical results, and extend
them to study instabilities in stretched and twisted filaments
that form solenoidal and plectonemic structures. We then study
active filaments such as snakes and other slender organisms by
solving inverse problems to identify optimal gaits for limbless
locomotion on solid surfaces and in bulk liquids.