Dynamics equation of the elastic rotation shaft possessed twain side is built basing on the principle of non-relative. The characteristics of equation include time-varying, strong coupling and high non-linear dynamic in engineering applications. In this paper, we establish primal space of system, aim space of system and mapping of topology contravariant between the two spaces according to the arithmetic of topology contravariant. Simple and decoupling aim space of system and the corresponding solution of contravariant topology are gained.