A numerically complicated geometro-dynamical system involving the global shape and energy of Eulers planar elastic curves is considered. In its analytic description this problem hinges on very delicate features of the Jacobian elliptic functions. This problem thus represents a very interesting challenge of merging together global information from several disciplines - geometry, variational calculus, special functions and highly nonlinear ODE theory - to understand the overall behaviour of the system. We are pursuing this challenge with all the available tools from computational mathematics.