  In this paper an alternative theory about space-time is given. First some preliminaries about 3-dimensional time and the reasons for its introduction are presented. Alongside the 3-dimensional space (S) the 3-dimensional space of spatial rotations (SR) is considered independently from the 3-dimensional space. Then it is given a model of the universe, based on the Lie groups of real and complex orthogonal 3x3 matrices in this 3+3+3-dimensional space. Special attention is dedicated for introduction and study of the space SxSR, which appears to be isomorphic to SO(3,R)xSO(3,R) or S^3xS^3. The influence of the gravitational acceleration to the spinning bodies is considered. Some important applications of these results about spinning bodies are given, which naturally lead to violation of Newton's third law in its classical formulation. The precession of the spinning axis is also considered. 
The geometry of the space-time and motion of the spinning bodies