Multilayer Coulomb Structures: Mathematical Principia of Microcosm Mechanics

The problem of a rotating planar multilayer structure with Coulomb interaction is formulated in the paper. The absence of solutions of the problem is proven. Based on this problem the method of constructing planar structures with differential rotation of the layers is developed. A number of structures are received and their dynamics and stability are studied by numerical methods with assistance of the system Galactica. The planar structures are unstable. Identified ways are found to improve the stability of multilayer structures and construct such structures, which could be models of atoms. The paper is of interest for specialists in the field of mechanics of microcosm and can be used by students when doing term papers and dissertations. The different mathematical methods are developed to solve problems in the mechanics of the microworld. They are in free access: http://www.ikz.ru/~smulski//Data/ClmRnStr/. In essence, the paper offers a new physics without theory of relativity and quantum mechanics. It aims for receiving a real knowledge of the microcosm. The paper is written in Russian. It is recommended to translate it into English, Chinese, Hindi, Persian and other national languages. This will allow the younger generation using the paper to cognize the real macrocosm.