Harnessing Active Force: The Pumping Mechanism of Child’s Swing Motion

Abstract

Life mechanics, an emerging field, focuses on the self-organizing motions manipulated by the mind within living systems. This study introduces the concept of 'active force’, generated by mind-body-environment interactions, as a fundamental driver underlying these self-organizing movements. As an example, we propose a new set of control equations to model the self-pumping swing motion by incorporating the active force into Newton's second law. With this new mechanical framework, we inversely derived the total (i.e., responsive) active force due to the body-environment interaction from the child’s swing motions with rapid standing and squatting movements. It revealed a pulse-like pattern of the total active force along the swing length, driving changes in the radial speed and swing length. This force counteracts the resistance and propels the swing, which is not attainable by the stone. Consequently, the active force serves as the foundational principle for self-organization in living systems, offering a novel mechanical approach for understanding and predicting extraordinary movements (e.g., sports and rehabilitation) regulated by the mind (e.g., nervous system) in biological systems.