Comprehensive classification of non-periodic relative motion styles of spacecraft: A geometric approach and applications

The classification of periodic relative motion in spacecraft dynamics is well-established, yet non-periodic motion remains underexplored. This paper addresses this gap by proposing a comprehensive classification model based on relative orbital dynamics. The elements of relative motion are defined, leveraging the characteristics of relative orbital dynamics to enable a detailed analysis of motion patterns. The analysis is then conducted from two perspectives: the geometrical configuration of the trajectory and the positional relationship between the trajectory and the spacecraft. A total of 19 motion styles are classified, including 14 non-periodic types, 3 periodic types, and 2 degenerate fixed-point cases, with corresponding dynamic conditions identified. Two representative applications demonstrate the practical utility of the classification: rapid target approach using flyby styles and hovering observation using droplet styles. Numerical simulations validate the accuracy of the classification and its applicability to real-world orbital scenarios. These findings provide a valuable framework for on-orbit services, such as formation flying, rendezvous, and orbital maintenance.