Hyperbolic chaos in a system of two Froude pendulums with alternating periodic braking

Abstract

We propose a new example of a system with a hyperbolic chaotic attractor. The system is composed of two coupled Froude pendulums placed on a common shaft rotating at constant angular velocity with braking by application of frictional force to one and other pendulum turn by turn periodically. A mathematical model is formulated and its numerical study is carried out. It is shown that attractor of the Poincaré stroboscopic map in a certain range of parameters is a Smale – Williams solenoid. The hyperbolicity of the attractor is confirmed by numerical calculations analyzing the angles of intersection of stable and unstable invariant subspaces of small perturbation vectors and verifying absence of tangencies between these subspaces.