The purpose of the work is to obtain new relationships in the mathematical model of perturbed motion of an articulated container carrier with a rudder frame on a pneumatic wheel during movement on technological roads of industrial enterprises. The main source of perturbations is skew-symmetric kinematic disturbances on the part of the inequalities of the covering of technological roads, which are approximated by harmonic functions along one track. The basis of the mathematical apparatus of the theoretical research is the methodology of analytical mechanics using the Lagrange equation of the second kind. The object of the study is reduced to a two-lobe dynamic system with two degrees of freedom, where the generalized coordinates are represented by linear and angular displacements of the container frame of the container carrier, which leads to the compilation of two differential equations of motion. The right-hand side of these equations describes the parameters of kinematic perturbation. From solving differential equations of perturbed motion of a container carrier with a rudder frame in the presence of skew-symmetric kinematic perturbations, the own dynamic characteristics of the system are obtained, the condition of loss of stability in transverse fluctuations of an articulated container carrier with a roller frame is recorded, a solving condition is obtained for determining the critical speed at which the system loses stability. The developed mathematical model contributes to the active intervention in power of the dynamical characteristics in the transverse vibrations of an articulated container carrier with a roller frame on the pneumatic wheel through the choice of the corresponding rigid characteristics of the stabilizer of transverse stability. Illustrative decoupling correlations demonstrate an algorithm of influence on system parameters at the stage of design development in order to create the perfect model of an articulated container carrier with a roller frame on a pneumatic wheel, which guarantees a great practical significance of the research.