Methodology for smooth-contact-modelling dynamic systems with angular inertia and energy dissipation: using a spinning top as a case study

Abstract This work presents a methodology for modelling multibody systems with contact/impact events, considering angular inertia and energy dissipation, using a spinning top in contact with a flat surface as a case study. This specific application is chosen due to its requirement for an extremely precise characterization of the contact interaction to ensure consistent results. The modelling process is carried out using smooth contact methods, incorporating the Hertz and Flores models for the normal force, and the Ambrósio and Gonthier models for tangential friction. To propose this methodology, an analysis and comparison of different models of normal and tangential forces will be performed, aiming to identify their differences and determine which are more appropriate for the system under study. Additionally, the impact of a variable restitution coefficient solution proposed by Ma et al. on the system’s dynamics is evaluated. This model, which was developed and tested by a finite element method tool and experiments, is now integrated within the context of a multibody dynamics model. The analysis addresses the effect of contact modelling on the evolution of the motion and the stability of the top. The results show that models with dissipation accelerate the cessation of rebounds and generate tighter trajectories, while models without dissipation produce prolonged oscillations and wider trajectories. Moreover, the impact of model selection on computational cost is discussed.