Mathematical Models in Physical Modeling.

The following questions are considered and answered: what should be the general models describing processes and phenomena studied when transforming them into critical equations forming a basis for physical modeling; how to set up these models; how to approach them; how do they differ from mathematical models used not for physical modeling; what are the advantages of transformation of general models into the criterial type, etc. This is illustrated on the example of analysis of a general mathematical model composed of 99 equations describing processes, their boundary and initial conditions. Transformations of this model by the methods of the theory of similarity into the criterial equation type, constituting a mathematical model of deformation in terms of similarity criteria, has shown that real bodies subjected to deformation are characterized by 14 similarity criteria. An example of incorrect use of the methods of the theory of similarity is given.