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Exotic dynamics of nonholonomic roller racer with periodic control. (English) Zbl 1412.37064

Summary: In this paper we consider the problem of the motion of the Roller Racer. We assume that the angle \(\varphi(t)\) between the platforms is a prescribed function of time. We prove that in this case the acceleration of the Roller Racer is unbounded. In this case, as the Roller Racer accelerates, the increase in the constraint reaction forces is also unbounded. Physically this means that, from a certain instant onward, the conditions of the rolling motion of the wheels without slipping are violated. Thus, we consider a model in which, in addition to the nonholonomic constraints, viscous friction force acts at the points of contact of the wheels. For this case we prove that there is no constant acceleration and all trajectories of the reduced system asymptotically tend to a periodic solution.

MSC:

37J60 Nonholonomic dynamical systems
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
70F25 Nonholonomic systems related to the dynamics of a system of particles
70E55 Dynamics of multibody systems
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