  In this paper we illustrate the potential role which relative limit cycles
may play in biolocomotion. We do this by describing, in great detail, an
elementary example of reduction of a lightly dissipative system modeling
crawling-type locomotion in 3D. The symmetry group SE(2) is the set of rigid
transformations of the horizontal (ground) plane. Given a time-periodic
perturbation, the system will admit a relative limit cycle whereupon each
period is related to the previous by a fixed translation and rotation along the
ground. This toy model identifies how symmetry reduction and dissipation can
conspire to create robust behavior in crawling, and possibly walking,
locomotion.
