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This paper presents the vibroimpact dynamics of an in-plane tethered subsatellite caused by sudden braking during deployment or retrieval. The full dynamics of the subsatellite are composed of its free-flight and the instantaneous impacts. At the moment of impact, the reflective angle of the subsatellite is envisioned to be equal to its incident angle such that the impact law is obtained. Then, the stability of the periodic vibroimpacts is analyzed using the composite Poincaré map. Further, the vibroimpact responses that do not exceed a specified region are numerically determined via the cell mapping method.