Abstract
In this paper we present the principles for a new method of quaternion factorization of the equilibrium equations for the transversally isotropic elasticity. Natural and artificial materials have anisotropy of physical properties. Many of them have transversal isotropy of elastic properties. Transversally isotropic materials are used in many technologies and industries, for example, in rock mechanics under permafrost conditions. Mathematical description of such materials involves the model of a transversally-isotropic material with 5 independent elastic constants. The equations of this model are more complicated than those for isotropic elasticity, and their analysis causes much more difficulties. One of the methods for analyzing such equations is factorization, i.e. reduction to the solution of simpler first-order equations.
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