This is to be contrasted with parabolic LCSs ( see below ), which are also shearless LCSs but prevail as stationary curves to the shear functional even under arbitrary variations.
2.
As noted above under hyperbolic LCSs, a global variational approach has been developed in two dimensions to capture elliptic LCSs as closed stationary curves of the material-line-averaged Lagrangian strain functional.
3.
In contrast to hyperbolic LCSs, however, parabolic LCSs satisfy more robust boundary conditions : they remain stationary curves of the material-line-averaged shear funcitonal even under variations to their endpoints.
4.
The geodesic approach, however, also sheds more light on the robustness of hyperbolic LCSs : hyperbolic LCSs only prevail as stationary curves of the averaged shear functional under variations that leave their endpoints fixed.
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