Abstract <p>This paper addresses the mathematical modeling of the dynamics of a mechanical system consisting of a finite number of articulated wheeled platforms—the so-called robotic train, consisting of a leading platform and an arbitrary number of passive trailers. The derivation employs Gauss’s principle of least constraint—a variational approach applicable to both holonomic and nonholonomic constraints. The resulting model is minimal in dimension and explicitly relates the drive torques of the leading platform to the accelerations of all links in the chain. This model can be used in mobile robot control systems. The paper provides a numerical example for a train of three platforms with estimates of the required drive torques, trajectory deviations, and computational load. The results obtained demonstrate the physical correctness of the model, as well as its suitability for integration into real controllers.</p>