  Gliding is a means of locomotion on rigid substrates utilized by a number of
bacteria includingmyxobacteria and cyanobacteria. One of the hypotheses
advanced to explain this motility mechanism hinges on the role played by the
slime filaments continuously extruded from gliding bacteria. This paper solves
in full a non-linear mechanical theory that treats as dissipative shocks both
the point where the extruded slime filament comes in contact with the
substrate, called the filament's foot, and the pore on the bacterium outer
surface from where the filament is ejected. We prove that kinematic
compatibility for shock propagation requires that the bacterium uniform gliding
velocity (relative to the substrate) and the slime ejecting velocity (relative
to the bacterium) must be equal, a coincidence that seems to have already been
observed.
