Application of SU(2) Group Fibration for Kinetic Problems of Polyatomic Molecules

Abstract

We point out the region in 3D-space permitted by symmetry that is available for the translational motion of rotating molecules. This region belongs to the one-parametric subgroup noted as fiber. It has the range of 0–1 for real variable and is disposed on the straight line directed by basic quaternion. The base part of fibration contains the two-dimensional sphere known as a symmetry structure which describes rotations of solid body. As an example of polyatomic molecules we use in this study water molecules. When water molecules are related to the fiber type of symmetry they must move in one direction pointed by basic quaternion in opposite to the three mutually orthogonal directions statistically adopted. The movement of molecules in one direction which, however, can be arbitrary oriented in 3D-space allow us to give the explanation of experimental results.