Purpose. Determination of the regularities in the variation of the coupling parameters of the wheel-rail pair and the energy consumption accompanying them, taking into account the thermophysical processes in the contact zone in the transmission of friction motion for various interaction conditions. methodology. An analytical model for the interaction of a wheel and a rail on an elementary contact spot is developed in the presence of normal and tractive effort. A dependence that describes the change in the average temperature at the contact spot of the wheel-rail pair on the locomotive speed is obtained. The current value of the elasticity modulus of the contacting pair material is determined as a contact time function. findings. Based on theoretical studies of the parameters of vehicle motion along the railroad track, a mathematical model of the tractive force realization for nonstationary rectilinear motion is formulated. To determine the influence degree of the temperature change on the contact spot of the wheel-rail pair associated with the speed of the locomotive motion and the relative speed of the output links, the dependences for the coefficient characterizing the tractive power of the vehicle are obtained. originality. Taking into account the thermophysical processes that occur during the interaction of contacting bodies, analytical dependencies have been obtained to determine the traction capacity for different movement speeds and the relative speed of the wheel and rail movement for main and mine locomotives. The dependencies suggested take into account the change in the properties of the surface layers of the contacting pair. Practical value. Knowledge of physics of the processes occurring in the contact zone of the wheel-rail pair will allow more accurately predicting the vehicles tractive properties, comparing possible options at the design stage and greatly accelerating the process of selecting the structural scheme. This will allow developing recommendations and proposals on modernization and improvement of existing vehicles.

Purpose. To improve both reliability and engineering accuracy of 3D modeling of a vehicle movement. methodology. Orts of natural trihedral of spiral-helix supporting trajectory are expressed vectorially by means of time derivatives of a radius vector of a program movement. Quaternion matrices represent the complicated operations of vector algebra. Spatial orientation or program rotation of a natural trihedral is described with the help of Gibbs vector, Rodriguez-Hamilton vector, matrix of direction cosines depending upon kinematic parameters of the program movement.findings. A hodograph of program transfer of a vehicle is represented in the class of spiral-helix supporting trajectories in terms of earth reference. Unit vectors of a natural trihedral of the spiral-helix supporting trajectory have been obtained depending on the time derivatives of the program motion hodograph.Originality. The program transfer -radius vector hodograph and program rotation (orientation) -Gibbs vector or quaternion on Rodriguez-Hamilton parameters are represented vectorially making it possible to model spatial orientation problems and problems of control of dynamic systems (i.e. vehicles) in the form of quaternion matrices.Practical value. Calculation formulas are represented in the ordered, compacted matrix form adapted directly to computer technology. The algorithm helps solve a wide range of problems of dynamic design of vehicles.