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The two LAGEOS and LARES are laser-ranged satellites tracked with the bestaccuracy ever achieved. Using their range measurements many geophysicalparameters were calculated and some General Relativity effects were directlyobserved. To obtain precise and refined measurements of the effects due to thepredictions of General Relativity on the orbit of these satellites, it ismandatory to model with high precision and accuracy all other forces, reducingthe free parameters introduced in the orbit determination. A main category ofnon-gravitational forces to be considered are those of thermal origin, whosefine modeling strongly depends on the knowledge of the evolution of the spinvector. We present a complete model, named LASSOS, to describe the evolution ofthe spin of the LAGEOS and LARES satellites. In particular, we solved Eulerequations of motion considering not-averaged torques. This is the most generalcase, and the predictions of the model well fit the available observations ofthe satellites spin. We also present the predictions of our model in thefast-spin limit, based on the application of averaged equations. The resultsare in good agreement with those already published, but with our approach wehave been able to highlight small errors within these previous works. LASSOSwas developed within the LARASE research program. LARASE aims to improve thedynamical model of the two LAGEOS and LARES satellites to provide very preciseand accurate measurements of relativistic effects on their orbit, and also tobring benefits to geophysics and space geodesy.

The LArase Satellites Spin mOdel Solutions (LASSOS): a comprehensive model for the spin evolution of the LAGEOS and LARES satellites