The development of scientific directions of mechanics as a result of research in analytical mechanics, space dynamics and applied mathematics is considered. The basic theorems of analytical dynamics were extended to mechanical systems of variable composition. The abstract concept of a point of variable mass is introduced in the form of a small area of space, endowed with mass, associated with the main body. The subject of consideration is a system of particles with constant masses, the composition of which varies. This allows one to take into account the change in mass and the internal movement of particles, leading to the creation of reactive forces.