Dynamic Modeling and Simulation of a Real World Billiard

TL;DR

This paper develops a mathematical model for real-world billiards with arbitrary boundaries, successfully matching experimental data for various shapes driven sinusoidally, advancing understanding of nonlinear dynamics in such systems.

Contribution

It introduces a simple, parameter-based model for realistic billiard dynamics that accurately predicts experimental results without complex energy assumptions.

Findings

Model accurately predicts billiard motion for different geometries.

Simulations match experimental data without exotic energy dependence.

Applicable to arbitrary boundary shapes in driven billiards.

Abstract

Gravitational billiards provide an experimentally accessible arena for testing formulations of nonlinear dynamics. We present a mathematical model that captures the essential dynamics required for describing the motion of a realistic billiard for arbitrary boundaries. Simulations of the model are applied to parabolic, wedge and hyperbolic billiards that are driven sinusoidally. Direct comparisons are made between the model's predictions and previously published experimental data. It is shown that the data can be successfully modeled with a simple set of parameters without an assumption of exotic energy dependence.