Nonlinear dynamics of a rotating SD oscillator

In this paper, we present a novel model which comprises a conventional pendulum and the presently proposed SD oscillator being of 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 SD oscillator. The unperturbed system behaves both standard (smooth) and nonstandard (discontinuous) nonlinear dynamics of equilibrium bifurcations, periodic patterns and their separatrices of homoclinic and heteroclinic orbits of the first type, second-type and double heteroclinic orbits. Chaotic attractors are presented when the system is excited under the perturbation of viscous damping and external harmonic forcing within smooth regime. The results presented herein this paper show the dependency of the demonstrate attractors depending the coupling strength of the the pendulum and the SD oscillator exhibiting pendulum-type, SD-type and their mixture.