Geodesic
Qualitative Analysis of the Traction Force of a Rotating Drive Wheel with a Weightless Tire
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 211-221

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A plane problem of controlled rotation of a wheel with a weightless tire is considered. The wheel is placed on a fixed base and is equipped with a shock absorber to damp vertical vibrations. For simplicity, horizontal motions of the rotation axis are not admitted. It is required to maximize the average traction force on a sufficiently long time interval by applying a bounded control torque on the rotation axis. A nonlinear mathematical model of the system is developed, with the tire modeled by a weightless solid hollow cylinder connected to the wheel disk by numerous weightless springs that are in a pretensioned state. Equations of motion are derived with the use of the quasistatic condition. The dynamics of the process and the maximum traction force are analyzed. 
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     author = {S. A. Reshmin},
     title = {Qualitative {Analysis} of the {Traction} {Force} of a {Rotating} {Drive} {Wheel} with a {Weightless} {Tire}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {211--221},
     publisher = {mathdoc},
     volume = {315},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2021_315_a14/}
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S. A. Reshmin. Qualitative Analysis of the Traction Force of a Rotating Drive Wheel with a Weightless Tire. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 211-221. http://geodesic.mathdoc.fr/item/TM_2021_315_a14/