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Gossamer-1 is the first project of the three-step Gossamer roadmap, the purpose of which is to develop, prove and demonstrate that solar-sail technology is a safe and reliable propulsion technique for long-lasting and high-energy missions. This paper firstly presents the structural analysis performed on the sail to understand its elastic behavior. The results are then used in attitude and orbital simulations. The model considers the main forces and torques that a satellite experiences in low-Earth orbit coupled with the sail deformation. Doing the simulations for varying initial conditions in attitude and rotation rate, the results show initial states to avoid and maximum rotation rates reached for correct and faulty deployment of the sail. Lastly comparisons with the classic flat sail model are carried out to test the hypothesis that the elastic behavior does play a role in the attitude and orbital behavior of the sail