The ISAS/JAXA Solar Power Sail mission, bound to explore the Jupiter trojans, will face many challenges during its journey. The landing manoeuvre is one of the most critical parts of any space mission that plans to investigate the surface of celestial bodies. Asteroids are mostly unknown bodies and in order to plan a successful landing on their surface, a great number of landing scenarios need to be taken into account. For the future mission to the Jupiter trojans, a study of the landing dynamics and their effects on the lander has to be done. A simple model of a lander has been created based on a design for the ISAS/JAXA Solar Power Sail mission, and the possible landing scenarios have been simulated. For this case, only the last part of the landing, which will be a free-fall has been taken into account. The lander is modelled as a rigid structure with a landing gear composed of four legs. The surface has been modelled as a flat plane with different inclinations and the possibility of including small obstacles or terrain roughness has been implemented. In the model, the lander is allowed 6 degrees of freedom. Several landing possibilities are tested with residual velocities and deviations in the starting point, and the stability of the lander is evaluated respect its geometry. Damping strategies have been considered to protect the instruments and reduce the impact, allowing for a safer landing. The effect of including crushable honeycomb dampers in the legs is also implemented, simulated and evaluated, by using a model of crushable honeycombs with different characteristics. In addition, the model includes also the position, direction and characteristics of the thrusters. Thus, it could be used to study other phases of the landing sequence where active control of the lander is needed, and evaluate the behaviour and response of different control-loop algorithms for attitude and position control of the lander.