Justification of the Principles of Coordinate Theory Based on the D'alembert's Principle and Small Movements

The work is a continuation of a number of author's studies devoted to the accuracy of determining the coordinates of an abstract object in technological space. So, since any object is in two coordinate systems, there is a problem of compatibility of these systems. It is this compatibility of coordinate systems that causes stability of motion and location of an abstract object in space. Now the stability of the movement or location of an object in space is taken as its frame of reference, that is, the zero point of any device or object. This is especially true for machine tools with numerical control (CNC). In order to solve the problem of compatibility of the coordinate system of the machine and the part, it is necessary to create a basic theory of coordinates, which will solve the problems of coordinating coordinate systems. The presence of an imaginary coordinate system in the CNC memory and the process of its implementation in a real machine coordinate system are shown. There is a need to investigate the physical and mathematical properties of a point, a dash, an error field structure and the relationship between all these field elements. The research proposed by the authors is devoted to the interpretation of ordinary natural phenomena by the physicochemical laws of interaction between abstract entities. Thus, the object of research is the relationship between imaginary and real coordinates. One of the most problematic places is the spatial reference of abstract space, that is, functional movement or stationary state. Analytical studies based on field affine transformations are used in this research. As a result, the possibility of creating a theory of coordinates of abstract objects in general, regardless of their physicochemical and medico-biological properties, has been theoretically substantiated. So, if to consider the processes of interaction between abstract objects, then it is possible to state the fact that such interaction has a very specific character. As a result, let's obtain a lot of sciences that give a similar description of the processes around us and their branches. It should be emphasized that there is a fairly clear distinction between the main scientific areas at the initial stage. The research carried out is useful in the development of metrological instruments and standard measuring instruments in assessing their stability