ABSTRACT
The method of averaging is a mathematically justified method of research and it is based on a number of strictly proven theorems [32, 51, 80, 123]. On the other hand, the method of averaging is based on the wide evidence of its successful practical application in the investigation of various problems. And due to its “physicality” the method of averaging was used in celestial mechanics and for problems of non-linear oscillations much earlier than it has been mathematically justified. Now the domain of application of the method of averaging is a little wider than the domain where it is justified. Thus, generally speaking, the results of researches can be incorrect and hence direct comparison with results of numerical integration of the complete equations is the only way of checking its validity.
