Dynamics of a system of coupled inverted pendula with vertical forcing

TL;DR

This paper investigates how interactions in a network of vertically forced inverted pendula affect their stability, revealing that interactions generally reduce stability but can lead to complex behaviors like beats and clustering.

Contribution

It provides a numerical analysis of many-body effects on the stability of coupled inverted pendula, highlighting the impact of different coupling schemes and system size.

Findings

Interaction degrades individual pendulum stability

Nearest neighbor coupling has a stronger destabilizing effect

System size increase improves overall stability

Abstract

Dynamical stabilization of an inverted pendulum through vertical movement of the pivot is a well-known counterintuitive phenomenon in classical mechanics. This system is also known as Kapitza pendulum and the stability can be explained with the aid of effective potential. We explore the effect of many body interaction for such a system. Our numerical analysis shows that interaction between pendula generally degrades the dynamical stability of each pendulum. This effect is more pronounced in nearest neighbour coupling than all-to-all coupling and stability improves with the increase of the system size. We report development of beats and clustering in network of coupled pendula.