A Rotating Pendulum Linked by an Oblique Spring

Abstract

We present a novel model which comprises a rotating pendulum linked by an oblique spring pinned to its rigid support. This model provides a cylindrical dynamical system with both smooth and discontinuous regimes depending on the value of a system parameter and also the dynamics transient relying on the coupling strength between the pendulum and the linked spring. The presented system behaves with both standard (smooth) and nonstandard (discontinuous) nonlinear dynamics of equilibrium bifurcations and the periodic patterns when it is unperturbed. Complicated resonant structures of period, quasi-period and stochastic phenomena are presented for the system with unique harmonic perturbation. The chaotic behavior of the system perturbed by both viscous-damping and external excitations is also demonstrated.