This article is cited in 1 paper

Realization of the brachistochronic motion of Chaplygin sleigh in a vertical plane with an unilateral nonholonomic constraint

Aleksandar M. Obradović^a, Oleg Yu. Cherkasov^bc, Luka N. Miličić^a, Slaviša Šalinić<sup>d

a</sup> Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia
^b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^c Faculty of Computational Mathematics and Cybernatics, Shenzhen MSU-BIT University, Shenzhen, P.R. China
^d Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Kraljevo, Serbia

Abstract: The paper considers the procedure for determining the brachistochronic motion of the Chaplygin sleigh in a vertical plane, where the blade is such that it prevents the motion of the contact point in one direction only. The position of the sleigh mass center and orientation at the final positions is specified, as well as the initial value of mechanical energy. The simplest formulation of a corresponding optimal control problem is given and it is solved by applying Pontryagin’s maximum principle. For some cases, analytical solutions of differential equations of the two-point boundary value problem (TPBVP) of the maximum principle were found. Numerical integration was carried out for other cases using the shooting method, where the assessment of missing terminal conditions was given and it was shown that the solution obtained represents the global minimum time for the brachistochronic motion. The method of the brachistochronic motion by means of a single holonomic and a single unilateral nonholonomic mechanical constraint is presented.

Keywords: Chaplygin sleigh, maximum principle, unilateral nonholonomic constraint, analytical solutions.

MSC: 70E18, 70Q05, 49N90

Received: 17.10.2023
Accepted: 29.11.2023

Language: English

DOI: 10.2298/TAM231017011O