To dynamics of variable-mass point

V.G.Veretennikov, V.A.Sinitsyn

Moscow aviation institute

Volokolamskoe highway, 4, Moscow, б-80, GSP-3, 125993

Russia

Models of the variable mass's point are used in researching the reactive movement, as well as in the rocket flight theory. The result of the first sum of K.A. Tsiolkovsky shows that an unlimited high speed may be imparted to a rocket in a free space within a certain period of time and, of course, the question arises of how the velocity equivalent to the speed of light can be reached. The scientific printed matters have been discussing the problems of creating such objects with the help of the reactive principle, which would possess high level of energy in conjunction with the complete loss of mass (it is a rather paradoxical situation for classical mechanics). Becoming more actual are the problems of flying at speeds at which one shouldn't ignore the relativistic effects, but the model of the relativistic point of variable mass (RPVM) has not been properly developed up to nowadays.

This article analyzes the energetic co-relations in the conditions of Ciolkovskii's classical task within the system: the point of variable mass (PVM) - changing mass (the separating particles right before their separation, and separated mass). Received finally is an expression of the reactive force's work imparted to PVM, creating the kinetic energy of PVM and kinetic energy of changing mass just before the separation of the particles. Also received is the expression of internal energy required to realize the reactive principle (subject to the reactive force's work applied to the separating particles). It was shown, that in case of the complete loss of mass (m R0) all work of the reactive forces in the system is fully aimed at the creation of the changing mass kinetic energy, and there is no need to introduce a new mass-free object possessed of energy.

A model of RPVM has been offered, which takes into consideration the changes in composition, variability of the relativistic mass, as well as the changes of the rest mass as a result of the current internal energy consumption. The equation of the energetic balance in the system is composed as follows: RPVM - relativistic separating particle, a transition is made towards a classical limit.