The use of the developed technology for solving inverse problems of parametric identification of the rotational motion of a spacecraft (SC) based on the accumulated sample of measurements of various compositions is expanded. On the example of processing telemetry data (measuring the direction vector to the Sun) of the BugSat-1 small spacecraft (SSC), the possibility of determining not only the characteristics of rotational motion but also its inertia coefficient is demonstrated. The rotational motion is determined based on the data obtained for five time intervals from January to May 2022, during which BugSat-1 made an uncontrolled movement around the direction vector toward the Sun. This type of motion does not allow applying traditional approaches to determine the dynamics of its rotation. In the process of data processing, a simplified model of the rotation of a SSC is used. At the same time, the initial conditions of rotational motion are estimated—the angular velocity vector and orientation angles, which made it possible to draw a conclusion about the precessional motion of a SSC. Using the analytical model of a regular precession, it is possible to estimate the inertia coefficient of a SSC. The results of flight information processing are presented and the errors of the obtained results are estimated.