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

TL;DR

This paper introduces the concept of active force generated by mind-body interactions as a key factor in understanding complex self-organizing movements in living systems, extending classical mechanics.

Contribution

It proposes a new mechanical framework incorporating active force into Newton's laws to model complex swing motions involving rapid movements.

Findings

Active force exhibits pulse-like patterns along the swing.

Active force drives changes in swing speed and length.

Active force counteracts resistance and propels the swing.

Abstract

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.