| soft slender structures are ubiquitous in natural and artificial systems and can be observed at scales that range from the nanometric to the kilometric , from polymers to space tethers . we present a general numerical approach to simulate the dynamics of filaments that , at every cross - section , can undergo all six possible modes of deformation , allowing the filament to bend , twist , shear and stretch , consistent with dynamics on the full euclidean group se(3 ) . additionally , we also account for the interaction of an active filament with itself and the environment via self - contact , surface friction and hydrodynamics . we examine the accuracy of our energy preserving and second order spatio - temporal method by means of a number of benchmark problems with known analytic solutions . finally , we demonstrate the capabilities of our approach both on passive physical problems related to solenoid and plectoneme formation in twisted , stretched filaments , and active biophysical problems in the context of limbless locomotion on solid surfaces and in bulk liquids . all together , our approach allows for a broad computational generalization of available methods to study the dynamics of soft filaments . |