  We present a novel application of rotors in geometric algebra to represent
the change of curvature tensor, that is used in shell theory as part of the
constitutive law. We introduce a new decomposition of the change of curvature
tensor, which has explicit terms for changes of curvature due to initial
curvature combined with strain, and changes in rotation over the surface. We
use this decomposition to perform a scaling analysis of the relative importance
of bending and stretching in flexible tubes undergoing self excited
oscillations. These oscillations have relevance to the lung, in which it is
believed that they are responsible for wheezing. The new analysis is
necessitated by the fact that the working fluid is air, compared to water in
most previous work. We use stereographic imaging to empirically measure the
relative importance of bending and stretching energy in observed self excited
oscillations. This enables us to validate our scaling analysis. We show that
bending energy is dominated by stretching energy, and the scaling analysis
makes clear that this will remain true for tubes in the airways of the lung.
