Proper time axis of a closed relativistic system

The definition of a proper time axis of a closed relativistic system of colliding particles is given. The solution of the proper time axis problem is presented. If the light velocity c equals the imaginary unit i, then in the case of a plane motion of the system the problem about the proper time axis turns out to be equivalent to the known in engineering mechanics problem about the reduction of any system of forces, applied to a rigid body, to the dynamic screw. In the general case, when c=i, the problem about the proper time axis turns out to be equivalent to the problem about the reduction to the dynamic screw of a system of forces, applied to a rigid body in a four-dimensional Euclidean space