Mechanical systems with hyperbolic chaotic attractors based on Froude pendulums

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.
Comment: Conference paper presented at International Scientific Conference "Scientific Heritage of Sergey A. Chaplygin: nonholonomic mechanics, vortex structures and hydrodynamics" (June 2-6, 2019, Cheboksary, Russia)