Modeling of a Rolling Flexible Circular Ring

The motion equations of a rolling flexible circular ring are derived using a Lagrangian formulation. The in-plane flexural and out-of-plane twist-bending free vibrations are modeled using the Rayleigh–Ritz method. The motion equations of a flexible circular ring translating and rotating in space are first developed and then constrained to roll on a flat surface by introducing Lagrange multipliers. The motion equations developed capture the nonholonomic nature of the circular ring rolling without slip on a flat surface. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the circular ring on its trajectory. The vibrations of the circular ring are observed to impact the ring's motion.