INTEGRABILITY OF THE EQUATIONS OF MOTION USING LOCAL INTEGRALS

Аннотация

In our previous paper [1], potential is obtained that admit local integrals of motion for steadystate stellar systems. The concept of a local integral, in contrast to D.Lynden-Bell [2], as a separate isolated surface, was introduced by V.A.Antonov [3] for an arbitrarily given field. Here we have the possibility of finding a trajectory in the presence of a local integral, in contrast to the true integral of motion with a local integral it is not always possible to completely find trajectories. As an example, using [1] we present the result of one of the cases of integrability of the equations of motion for a space model.