Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control
Ivan A. Bizyaevab, Alexey V. Borisova, Ivan S. Mamaevc
a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
c M. T. Kalashnikov Izhevsk State Technical University,
ul. Studencheskaya 7, Izhevsk, 426069 Russia
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.
Roller Racer, speed-up, nonholonomic mechanics, Rayleigh dissipation function, viscous friction, integrability by quadratures, control, constraint reaction force
|Russian Foundation for Basic Research
|Ministry of Education and Science of the Russian Federation
|The work of I.A. Bizyaev (Sections 1 and 3) was supported by the RFBR grant No. 18-38-00344 mol_a and was carried out at MIPT under project 5–100 for state support for leading universities of the Russian Federation. The work of A.V. Borisov (Section 2) was supported by the RFBR grant no. 18-08-00999-a. The work of I.S. Mamaev (Section 4) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2405.2017/4.6).
MSC: 37J60, 37C10
Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control”, Regul. Chaotic Dyn., 23:7-8 (2018), 983–994
Citation in format AMSBIB
\by Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev
\paper Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control
\jour Regul. Chaotic Dyn.
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