The problem of acceleration in the dynamics of a double-link wheeled vehicle with arbitrarily directed periodic excitation

This study investigates the motion of a nonholonomic mechanical system that consists of two wheeled carriages articulated by a rigid frame. There is a point mass which oscillates at a given angle $\alpha$ to the main axis of one of the carriages. As a result, periodic excitation occurs in the system. The equations of motion in quasi-velocities are obtained. Eventually, the dynamics of a double-link wheeled vehicle is modeled by a system that defines a non-autonomous flow on a three-dimensional phase space. The behavior of integral curves at large velocities depending on the angle $\alpha$ is investigated. We use the generalized Poincaré transformation and reduce the original problem to the stability problem for the system with a degenerate linear part. The proof of stability uses the restriction of the system to the central manifold and averaging by normal forms up to order 4. The range of values of $\alpha$ for which one of the velocity components increases indefinitely is found and asymptotics for the solutions of the initial dynamical system is determined.