Stabilizing Function of Skeletal Muscles: an Analytical Investigation

Stability is the ability of a system to return to its original state after a disturbance. Taking vertical oscillations of the centre of mass of a human bending his legs as an example we prove that the intrinsic mechanical properties of musculature can stabilize the oscillatory movement (preflex) without reflexive changes in activation. The human is represented by a model consisting of a massless two-segment linkage system (knee) topped by a point mass. Conditions for stability are calculated analytically based on the theory of Ljapunov and the results are illustrated by numerical examples. In order to guarantee a self-stabilizing ability of the muscle–skeletal system, the muscle properties such as force–length relationship, force–velocity relationship and the muscle geometry must be tuned to the geometric properties of the linkage system.