Types and stability of quasi-periodic response of a spherical pendulum

This study concentrates to an effect usually called quasi-periodic response. Double degree of freedom (DDOF) spherical pendulum as an auto-parametric system is used to demonstrate and investigate this effect. Sweeping the excitation frequency throughout the auto-parametric resonance interval, various types of quasi-periodic response can be encountered. An analytical–numerical approach of these effects is developed using the original non-linear system. Relevant differential system in “slow time” is presented, which provides periodic, orbital and a few singular solutions separating basic response types. Numerical evaluation of typical cases and comprehensive parametric study are included. Some open problems are indicated.

► Auto-parametric model of double degree of freedom spherical pendulum is studied. ► Analytical–numerical approach is developed for the non-linear system. ► Periodic, orbital and singular solutions are shown. ► Dynamic stability of the system is assessed.