THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT
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.
Keywords:
Chaplygin sleigh / maximum principle / unilateral nonholonomic constraint / analytical solutionsSource:
9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023, 2023, T.4.3-Publisher:
- Belgrade : Serbian Society of Mechanics
Funding / projects:
- Ministry of Science, Technological Development and Innovation of the Republic of Serbia, institutional funding - 200105 (University of Belgrade, Faculty of Mechanical Engineering) (RS-MESTD-inst-2020-200105)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Obradović, Aleksandar AU - Cherkasov, Oleg AU - Miličić, Luka PY - 2023 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6897 AB - 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. PB - Belgrade : Serbian Society of Mechanics C3 - 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023 T1 - THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT SP - T.4.3 UR - https://hdl.handle.net/21.15107/rcub_machinery_6897 ER -
@conference{ author = "Obradović, Aleksandar and Cherkasov, Oleg and Miličić, Luka", year = "2023", 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.", publisher = "Belgrade : Serbian Society of Mechanics", journal = "9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023", title = "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT", pages = "T.4.3", url = "https://hdl.handle.net/21.15107/rcub_machinery_6897" }
Obradović, A., Cherkasov, O.,& Miličić, L.. (2023). THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023 Belgrade : Serbian Society of Mechanics., T.4.3. https://hdl.handle.net/21.15107/rcub_machinery_6897
Obradović A, Cherkasov O, Miličić L. THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT. in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023. 2023;:T.4.3. https://hdl.handle.net/21.15107/rcub_machinery_6897 .
Obradović, Aleksandar, Cherkasov, Oleg, Miličić, Luka, "THE BRACHISTOCHRONIC MOTION OF CHAPLYGIN SLEIGH IN A VERTICAL PLANE WITH UNILATERAL NONHOLONOMIC CONSTRAINT" in 9 th International Congress of Serbian Society of Mechanics Vrnjačka Banja, Serbia, July 5-7, 2023 (2023):T.4.3, https://hdl.handle.net/21.15107/rcub_machinery_6897 .