A limit-cycle model of leg movements in cross-country skiing and its adjustments with fatigue

Using dynamical modeling tools, the aim of the study was to establish a minimal model reproducing leg movements in cross-country skiing, and to evaluate the eventual adjustments of this model with fatigue. The participants (N = 8) skied on a treadmill at 90% of their maximal oxygen consumption, up to exhaustion, using the diagonal stride technique. Qualitative analysis of leg kinematics portrayed in phase planes, Hooke planes, and velocity profiles suggested the inclusion in the model of a linear stiffness and an asymmetric van der Pol-type nonlinear damping. Quantitative analysis revealed that this model reproduced the observed kinematics patterns of the leg with adequacy, accounting for 87% of the variance. A rising influence of the stiffness term and a dropping influence of the damping terms were also evidenced with fatigue. The meaning of these changes was discussed in the framework of motor control.