Dynamical modelling of rubble pile asteroids using data-driven techniques

Context. Most asteroids are likely rubble pile asteroids (i.e. aggregates of loosely consolidated material). Their dynamics are hard to model due to their granular nature leading to a complex multi-scale and multi-regime system. Aims. This paper proposes a new data-driven methodology that aims to provide an analytical dynamical model of rubble pile asteroids using data coming from different numerical simulations. This analytical model will allow for the use of tools from the dynamical systems theory in order to investigate the results of the simulations while also providing more general results outside of what is contained within the training data. Methods. We use a novel technique called sparse identification of nonlinear dynamics (SINDy) to obtain an analytical model. The data used originate from high-fidelity and numerically complex discrete element simulations that take into account the contact interactions of non-spherical particles and their gravitational forces. Results. We find a simple analytical model that is accurate across various dynamical regimes. The dynamical model was used to characterise the phase space of the system, and we found that the stable region shrinks as the angular momentum increases. This allows for the determination of the critical angular momentum limit for asteroids with different shapes and bulk densities, and what the dynamical fate is of the asteroid after it reaches this limit. Conclusions. This work shows that SINDy is capable of modelling the dynamics of rubble pile asteroids, thus allowing for the characterisation of the phase space using techniques from dynamical systems theory such as finite time Lyapunov exponents.