A physical perturbation based study on the prediction of free-fall disks with chaotic modes in the water

TL;DR

This study investigates how physical perturbations influence the predictability of free-fall disks with chaotic motion in water, revealing that certain perturbations can enhance certainty and proposing a criterion for prediction reliability.

Contribution

It introduces a novel understanding of physical perturbations' role in chaotic free-fall motion and proposes a practical criterion for assessing prediction credibility.

Findings

Physical perturbations can improve the certainty of chaotic free-fall predictions.

A temporal criterion for prediction reliability is established.

Experimental verification supports the hypothesis.

Abstract

We report a phenomenon that physical perturbations sometimes can benefit the certainty of a free-fall motion with chaotic modes, albeit, as commonly believed, they can ruin it. We statistically compare those factors that may lead to uncertainty, by which we find that the growth of the standard deviation of the landing locations is directly determined by the physical perturbations. A significant yardstick is defined in the meantime. This temporal criterion is of big relevance to the replicability of such problems experimentally, although they are inherently chaotic. Our hypothesis is verified by experiments from other literature. This outcome also provides a practical strategy to evaluate the credible prediction time by estimating the disturbances from physical parameters as a priori.