Mathematical Model on Impact of Reynolds Number on Cascading Balls
DOI:
https://doi.org/10.62054/ijdm/0301.09Abstract
This study develops a rigorous mathematical framework to quantify the influence of Reynolds number on cascading ball dynamics in rhythmic throwing and juggling systems. Building on classical projectile motion and Lagrangian mechanics, the model explicitly incorporates aerodynamic drag as a Reynolds-number dependent force. By linking drag coefficients to flow regimes ranging from laminar to turbulent, the analysis reveals how Reynolds variation alters flight time, trajectory shape, and rhythmic synchronization conditions. The framework is extended to an arbitrary number of balls, including the dense-limit case where the number of balls approaches infinity. Numerical simulations demonstrate that increasing Reynolds number systematically reduces flight duration and trajectory height, while preserving rhythmic stability through compensatory timing adjustments. The results establish Reynolds number as a governing parameter in cascading dynamics, providing a physically grounded bridge between classical mechanics, fluid dynamics, and rhythmic coordination. This work offers new insights into the robustness of juggling motions and provides a scalable foundation for applications in biomechanics, robotics, and flow-sensitive rhythmic systems
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