This paper presents the analysis of a third-order linear differential equation representing the control of a muscle-tendon system, during quiet standing. The conditions of absolute stability and critical damping are analyzed. This study demonstrates that, for small oscillations, when the gravitational effect is modeled as a destabilizing negative stiffness and muscle-tendon stiffness is positive, the energy required to reach a critically damped state is very high. The high energy consumption is a consequence of a specific high threshold of muscle-tendon stiffness needed to achieve critical damping.
An approximated graphical method confirms that during a hold and release paradigm intended to perturb quiet standing, the ankle response to fall recovery is proper of a third-order system. Furthermore, a direct estimation of the muscle and tendon parameters was obtained.