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This lecture delves into the Ariane 501 case study, analyzing the first launch of the Ariane 5 rocket in 1996. It covers the events leading to the launch failure, focusing on the software errors and system complexities that caused the mission to end in an explosion. The presentation explores the trajectory correction, the role of the Inertial Reference System (IRS), the flight control system, and the software verification process. It also discusses the consequences of the failure, the investigation that followed, and the lessons learned for future space missions.