  The two LAGEOS and LARES are laser-ranged satellites tracked with the best
accuracy ever achieved. Using their range measurements many geophysical
parameters were calculated and some General Relativity effects were directly
observed. To obtain precise and refined measurements of the effects due to the
predictions of General Relativity on the orbit of these satellites, it is
mandatory to model with high precision and accuracy all other forces, reducing
the free parameters introduced in the orbit determination. A main category of
non-gravitational forces to be considered are those of thermal origin, whose
fine modeling strongly depends on the knowledge of the evolution of the spin
vector. We present a complete model, named LASSOS, to describe the evolution of
the spin of the LAGEOS and LARES satellites. In particular, we solved Euler
equations of motion considering not-averaged torques. This is the most general
case, and the predictions of the model well fit the available observations of
the satellites spin. We also present the predictions of our model in the
fast-spin limit, based on the application of averaged equations. The results
are in good agreement with those already published, but with our approach we
have been able to highlight small errors within these previous works. LASSOS
was developed within the LARASE research program. LARASE aims to improve the
dynamical model of the two LAGEOS and LARES satellites to provide very precise
and accurate measurements of relativistic effects on their orbit, and also to
bring benefits to geophysics and space geodesy.
