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We illustrate a procedure based on the Magnus expansion for studying mechanical problems which\udlead to non-autonomous systems of linear ODE’s. The effectiveness of the Magnus method is enlighten by the\udanalysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. In particular, for\udan isotropic compressible elastic tube subject to an azimuthal shear primary deformation we study the\udpossibility of axially periodic twist-like bifurcations. The approximate matricant of the resulting differential\udproblem and the first singular value of the bifurcating load corresponding to a non-trivial bifurcation are\uddetermined by employing a simplified version of the Magnus method, characterized by a truncation of the\udMagnus series after the second term

Geometric numerical integrators based on the Magnus expansion in bifurcation problems for non-linear elastic solids