The brachistochronic motion of a heavy ball rolling along an imperfect rough surface
Апстракт
The problem of brachistochronic motion of a heavy uniform ball rolling without slip along the upper outside surface of an imperfect rough stationary sphere, is solved. The control forces are located in the tangential plane, and their total power equals zero. In the first part of the paper the determination of the brachistochronic motion is solved as the problem of optimal control using Pontryagin’s maximum principle. This solution corresponds to the motion of the heavy ball along a perfect rough sphere. The second part provides the case when the constraint between the sphere and the ball is imperfectly rough. Here, the problem of optimal control is formulated in such way that the tangential component of the reaction of constraint is taken for the control, with the restriction resulting from Coulomb’s laws of sliding friction. The problem thus formulated belongs to the theory of singular optimal controls, and the solution that satisfies the Maximum principle consists of a singular part ...and a nonsingular part.
Извор:
Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia, 2020, 112-128Издавач:
- SERBIAN ACADEMY OF NONLINEAR SCIENCES
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200108 (Универзитет у Крагујевцу, Машински факултет, Краљево) (RS-MESTD-inst-2020-200108)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Obradović, Aleksandar AU - Šalinić, Slaviša PY - 2020 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3992 AB - The problem of brachistochronic motion of a heavy uniform ball rolling without slip along the upper outside surface of an imperfect rough stationary sphere, is solved. The control forces are located in the tangential plane, and their total power equals zero. In the first part of the paper the determination of the brachistochronic motion is solved as the problem of optimal control using Pontryagin’s maximum principle. This solution corresponds to the motion of the heavy ball along a perfect rough sphere. The second part provides the case when the constraint between the sphere and the ball is imperfectly rough. Here, the problem of optimal control is formulated in such way that the tangential component of the reaction of constraint is taken for the control, with the restriction resulting from Coulomb’s laws of sliding friction. The problem thus formulated belongs to the theory of singular optimal controls, and the solution that satisfies the Maximum principle consists of a singular part and a nonsingular part. PB - SERBIAN ACADEMY OF NONLINEAR SCIENCES C3 - Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia T1 - The brachistochronic motion of a heavy ball rolling along an imperfect rough surface EP - 128 SP - 112 UR - https://hdl.handle.net/21.15107/rcub_machinery_3992 ER -
@conference{ author = "Obradović, Aleksandar and Šalinić, Slaviša", year = "2020", abstract = "The problem of brachistochronic motion of a heavy uniform ball rolling without slip along the upper outside surface of an imperfect rough stationary sphere, is solved. The control forces are located in the tangential plane, and their total power equals zero. In the first part of the paper the determination of the brachistochronic motion is solved as the problem of optimal control using Pontryagin’s maximum principle. This solution corresponds to the motion of the heavy ball along a perfect rough sphere. The second part provides the case when the constraint between the sphere and the ball is imperfectly rough. Here, the problem of optimal control is formulated in such way that the tangential component of the reaction of constraint is taken for the control, with the restriction resulting from Coulomb’s laws of sliding friction. The problem thus formulated belongs to the theory of singular optimal controls, and the solution that satisfies the Maximum principle consists of a singular part and a nonsingular part.", publisher = "SERBIAN ACADEMY OF NONLINEAR SCIENCES", journal = "Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia", title = "The brachistochronic motion of a heavy ball rolling along an imperfect rough surface", pages = "128-112", url = "https://hdl.handle.net/21.15107/rcub_machinery_3992" }
Obradović, A.,& Šalinić, S.. (2020). The brachistochronic motion of a heavy ball rolling along an imperfect rough surface. in Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia SERBIAN ACADEMY OF NONLINEAR SCIENCES., 112-128. https://hdl.handle.net/21.15107/rcub_machinery_3992
Obradović A, Šalinić S. The brachistochronic motion of a heavy ball rolling along an imperfect rough surface. in Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia. 2020;:112-128. https://hdl.handle.net/21.15107/rcub_machinery_3992 .
Obradović, Aleksandar, Šalinić, Slaviša, "The brachistochronic motion of a heavy ball rolling along an imperfect rough surface" in Proceedings of the 1st CONFERENCE ON NONLINEARITY, October11–12, 2019, Belgrade, Serbia (2020):112-128, https://hdl.handle.net/21.15107/rcub_machinery_3992 .