A statistical sparse jump model for automatic identification of dynamical transitions in the co-orbital regime

Co-orbital dynamics appears in the three-body problem and is widely studied to analyze asteroidal behaviors, but also to design trajectories for interplanetary missions. It involves complex transitions that can be challenging to analyze manually in case of large and lengthy dataset, typically of planetary science, but also in case of parametric analysis that involves different perturbations. For this reason, in this work we employ the statistical sparse jump model, an efficient and robust machine learning model, to classify co-orbital regimes and identify their transitions. The ability of the model to estimate regime-specific parameters and ensure regime persistence provides a significant advantage in capturing the dynamics of these motions. Unlike black-box methods, this model offers interpretable results directly linked to the physical parameters of celestial mechanics. Our method achieves high accuracy in simpler cases and strong performance in more complex scenarios, even with large datasets. Applications to data corresponding to real and simulated trajectories reveal critical insights into the co-orbital dynamics, such as the average duration of regimes and the role of key orbital parameters. This work marks the first application of statistical sparse jump models in orbital dynamics, and contributes to bridge machine learning with celestial mechanics.