Beyond Newtonian Mechanics: An Exploration of Active Force in Complex Swing Motions

Life mechanics, an emerging field, focuses on the self-organizing forces and motions within living systems. This study introduces the novel concept of active force, generated by mind-body interactions, as an essential element in understanding self-organizing movements. 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 analyzed the child's complex swing motions with rapid standing and squatting movements. The results reveal a pulse-like pattern of the active force along the swing length, driving changes in the radial speed and swing length. This active force counteracts the resistance and propels the swing, which is not attainable by the stone. Thus, active force underlies self-organization in living systems, warranting further exploration of its mechanics in life movements.