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 nongravitational 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.

• Received 1 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.044034