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Twisted rods, helices and buckling solutions in three dimensions

The study of slender elastic structures is an archetypical problem in continuum mechanics, dynamical systems and bifurcation theory, with a rich history dating back to Euler's seminal work in the 18th century. These filamentary elastic structures have widespread applications in engineering and biology, examples of which include cables, textile industry, DNA experiments, collagen modelling etc. One is typically interested in the equilibrium configurations of these rod-like structures, their stability and dynamic evolution and all three questions have been extensively addressed in the literature. However, it is generally recognized that there are still several open non-trivial questions related to three-dimensional analysis of rod equilibria, inclusion of topological and positional constraints and different kinds of boundary conditions.