Mechanical systems with hyperbolic chaotic attractors based on Froude pendulums

TL;DR

This paper introduces two novel mechanical systems based on Froude pendulums that exhibit hyperbolic chaotic attractors of Smale-Williams type, confirmed through numerical simulations and hyperbolicity checks.

Contribution

The paper presents new mechanical models with hyperbolic chaos based on Froude pendulums, expanding the understanding of chaotic attractors in physical systems.

Findings

Models exhibit Smale-Williams type chaotic attractors

Parameter regions for hyperbolic chaos identified

Numerical verification confirms hyperbolicity

Abstract

We discuss two mechanical systems with hyperbolic chaotic attractors of Smale - Williams type. Both models are based on Froude pendulums. The first system is composed of two coupled Froude pendulums with alternating periodic braking. The second system is Froude pendulum with time-delayed feedback and periodic braking. We demonstrate by means of numerical simulations that proposed models have chaotic attractors of Smale - Williams type. We specify regions of parameter values at which the dynamics corresponds to Smale - Williams solenoid. We check numerically hyperbolicity of the attractors.