Aleksandar Obradović, Slaviša Šalinić, Radoslav Radulović, “The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip”, Theor. Appl. Mech., 2017, Volume 44, Issue 2,Pages <nobr>237

This article is cited in 4 papers

The brachistochronic motion of a vertical disk rolling on a horizontal plane without slip

Aleksandar Obradović^a, Slaviša Šalinić^b, Radoslav Radulović^a

^a Department of Mechanics, Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia
^b Department of Applied Mechanics, Mathematics and Physics, Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Kraljevo, Serbia

Abstract: This paper deals with the brachistochronic motion of a thin uniform disk rolling on a horizontal plane without slip. The problem is formulated and solved within the frame of the optimal control theory. The brachistochronic motion of the disk is controlled by three torques. The possibility of the realization of the brachistochronic motion found in presence of Coulomb dry friction forces is inspected. Also, the influence of values of the coefficient of dry friction on the structure of the extremal trajectory is analyzed. Two illustrative numerical examples are provided.

Keywords: brachistochronic motion, nonholonomic constraints, Coulomb dry friction, optimal control, rolling without slip.

MSC: 70E18, 70Q05

Received: 02.10.2017
Revised: 24.11.2017

Language: English

DOI: 10.2298/TAM171002015O