  The physical and bio-mechanical principles that govern undulatory movement on
wet surfaces have important applications in physiology, physics, and
engineering. The nematode {\it C. elegans}, with its highly stereotypical and
functionally distinct sinusoidal locomotory gaits, is an excellent system in
which to dissect these properties. Measurements of the main forces governing
the {\it C. elegans} crawling gait on lubricated surfaces have been scarce,
primarily due to difficulties in estimating the physical features at the
nematode-gel interface. Using kinematic data and a hydrodynamic model based on
lubrication theory, we calculate both the surface drag forces and the
nematode's bending force while crawling on the surface of agar gels. We find
that the normal and tangential surface drag force coefficients during crawling
are approximately 220 and 22, respectively, and the drag coefficient ratio is
approximately 10. During crawling, the calculated internal bending force is
time-periodic and spatially complex, exhibiting a phase lag with respect to the
nematode's body bending curvature. This phase lag is largely due to viscous
drag forces, which are higher during crawling as compared to swimming in an
aqueous buffer solution. The spatial patterns of bending force generated during
either swimming or crawling correlate well with previously described
gait-specific features of calcium signals in muscle. Further, our analysis
indicates that changes in the motility gait of {\it C. elegans} is most likely
due to the nematode's adaptive response to environments characterized by
different drag coefficient ratios.
