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Interaction between a robot and Bunimovich stadium billiards.

J V A Vasconcelos1, L H Miranda-Filho1, A J F de Souza1

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Area of Science:

  • Physics
  • Robotics
  • Chaos Theory

Background:

  • Classical mechanics and chaos theory offer insights into complex systems.
  • The robot-environment-task framework facilitates novel experimental approaches.
  • Bunimovich stadium billiards are a standard model for studying deterministic chaos.

Purpose of the Study:

  • To experimentally observe and quantify chaotic dynamics in a macroscopic billiard system.
  • To validate theoretical predictions of chaos using empirical data.
  • To investigate the sensitivity of the system to initial conditions.

Main Methods:

  • A macroscopic 3.38-m long Bunimovich stadium billiard setup was used.
  • A robot interacted with the billiard system, with specular reflection.
  • A digital video camera recorded the dynamic time evolution for data analysis.
  • The Lyapunov exponent was calculated from experimental time series data.

Main Results:

  • Experimental results for the Lyapunov exponent showed concordance with theoretical predictions.
  • The Poincaré surface of section was successfully determined from experimental data.
  • The sensitivity to initial conditions was analyzed as a function of time.

Conclusions:

  • The experiment successfully demonstrated and quantified chaotic behavior in a macroscopic billiard system.
  • The findings support the theoretical framework of chaos in classical mechanics.
  • The methodology provides a robust approach for studying complex dynamical systems.