The manuscript presents a trajectory method for describing the rotations of surface crystals such as fullerenes, nanotubes, and nanotori. This method does not require the implementation of successive rotations of the considered molecular structures around the axes of the selected basis. Therefore, it is free from the shortcomings of the approaches of Euler and Hamilton. On its basis, an efficient algorithm for calculating the motions of a magneto-susceptible fullerene in an alternating magnetic field has been developed. The nature of rotation of fullerenes in fields of various configurations has been studied.