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Abstract Solar wind directional discontinuities, such as rotational discontinuities (RDs), significantly influence energy and transport processes in the Earth's magnetosphere. A recent observational study identified a long‐lasting double cusp precipitation event associated with RD in solar wind on 10 April 2015. To understand the magnetosphere‐ionosphere response to the solar wind RD, a global hybrid simulation of the magnetosphere was conducted, with solar wind conditions based on the observation event. The simulation results show significant variations in the magnetopause and cusp regions caused by the passing RD. After the RD propagates to the magnetopause, ion precipitation intensifies, and a double cusp structure at varying latitudes and longitudes forms near noon in the northern hemisphere, which is consistent with the satellite observations by Wing et al. (2023,https://doi.org/10.1029/2023gl103194). Regarding dayside magnetopause reconnection, the simulation reveals that the high‐latitude reconnection process persists during the RD passing, regardless of whether the interplanetary magnetic field (IMF) with a highB_y/B_zratio has a positive or negativeB_zcomponent, and low‐latitude reconnection occurs after the RD reaches the magnetopause at noon when the IMF turns southward. By examining the ion sources along the magnetic field lines, a connection is found between the single‐ or double‐cusp ion precipitation and the solar wind ions entering from both high‐latitude and low‐latitude reconnection sites. This result suggests that the double‐cusp structure can be triggered by magnetic reconnection occurring at both low latitudes and high latitudes in the opposite hemispheres, associated with a largeB_y/B_zratio of the IMF around the RD.