In this thesis, kinematic reconstruction of satelite rotational motion is described, which is implemented to real RAX-1 nanosatellite. In the begining, rigid body motion is written in matrix form and described in terms of SE(3) group. After that, SO(3) group is described, which represents rotational motion of rigid body. Since parameterization using SO(3) group uses nine parameters, only three of which are independent, parametrization in terms of Euler angles is showed. The fact that singularities appear when three-parameter parametrization is used to describe 3D rotational motion (e.g. Euler angles), there is a need to introduce quaternions, which are singularity-free. Constraining the quaternion to unit norm, we get unit quaternion, which can also include Euler parameters. Furthermore, two standard methods for numerical integration on quaternions are introduced, along with new method, in which unit norm of quaternion is implicitly satisfied and therefore there is no need to introduce additional algebraic equation, which should lead to increased efficiency in numerical integration. At the end, kinematic reconstruction of real RAX-1 nanosatellite is made, during which two integration methods are compared - new method and method in which unit norm of quaternion is explicitly satisified.