The article describes design diagrams of four-axle rail flat car with two anti-symmetrically located heavy cargos with elastic dissipative elements (supports), whose common center of mass coincides with the center of mass of a flat car. The authors pose a problem of safety of a flat car’s movement, caused by dislocation of the center of mass of cargo, its weight, speed of movement, certain parameters of elastic and dissipative supports, with regard to stability of the wheel against possible derailment and risk of transversal dumping of a car in rail track’s curves due to transversal horizontal forces. It is the reason to study, first of all by theoretically, the dynamics of a car, to determine admissible limits of transversal and longitudinal dislocation of the center of mass of cargo with regard to the axis of symmetry of a car, and to find rational parameters of elastic and dissipative supports for cargo that ensure safety of traffic.

The developed design diagrams are based on the mechanical system «flat car – cargo» that includes 13 solid bodies (car frame, two cargos, four side frames, two bars over springs, four wheelsets of two bogies). The authors studied bouncing, rocking, rolling, side drifting, wobbling of a car and cargo, as well as bouncing, rocking, rolling of side frames of bogies and wobbling of bogies.

The authors propose algebraic expressions to determine deformation of spring sets and supports for cargo, deformation of the track with determined vertical and horizontal irregularities, reaction of the rail to the wheels’ impact (if there are quenching forces of viscous friction and unilateral relation of wheels and rails), and vertical and horizontal forces influencing spring sets and elastic dissipative supports for cargo.

In order to develop differential equations the researchers used d’Alambert’s principle. They developed a system of 23 differential equations, describing spatial oscillation of a flat car.