Can Anisotropic Friction Induce Chaos in a Horizontal Pendulum on a Rotating Disk?

Abstract

Yes – anisotropic friction can induce chaotic motion in a horizontal pendulum on a rotating disk, under appropriate conditions. Although parameters required for chaotic motion are not common in engineering practice, i.e., a large anisotropy ratio and low bearing friction. In order to demonstrate this phenomenon, a dimensionless model of the system is developed, in which the pendulum’s tip slides on a rotating disk, and the anisotropic friction properties result from the disk surface structure. The model is explored numerically by time integration, complemented by bifurcation diagrams, Poincaré maps and estimates of Lyapunov characteristic exponents. The results demonstrate that when friction deviates from being co-linear with the sliding direction, the system undergoes a loss of static equilibria and follows limit cycles. As system parameters vary, these cycles undergo period-doubling bifurcations and evolve into chaotic attractors. The emergence of chaos is robust within specific, bounded regions of the system’s parameter space, but is sensitive to additional energy dissipation, i.e., adding moderate viscous damping in the pendulum joint suppresses chaotic dynamics and restores simpler periodic behavior. These findings establish anisotropic friction as a mechanism capable of generating rich nonlinear dynamics in an otherwise simple mechanical setup. The outcome of this study has practical implications, demonstrating that surface anisotropy can be regarded as a controllable factor. This can be utilized to produce complex responses which are desirable, for instance, in energy harvesting. On the other hand, friction anisotropy should be minimized where predictable, stable performance is required.