 Material frame of a rod

A right-handed orthonormal frame attached to the cross-sections of an elastic rod. For an unshearable elastic rod, ${\mathbf{d}}_3$ is the unit tangent vector to its centreline, while ${\mathbf{d}}_1$ and ${\mathbf{d}}_2$ follow the orientation of its material cross-section. Unlike a frame constructed only from the centreline curvature, the material frame records the twist of the material about the tangent.