Differential equations of the start of motion of elasticly coupled inert bodies on the example of a train with elastic couplings

The starting mode for a ground vehicle is the most difficult. An effective way to pull off a train is to select coupling clearances. In this case, the cars are set in motion consequently, and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method, however, has two significant drawbacks - a small fixed value of the gaps in the couplings, which limits the effectiveness of the method and the shock nature of the impulse transmission, which negatively affects the state of the structural elements of the train. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the starting mode of the train is essentially due to the replacement of the simultaneous starting of the sections with alternate ones.