On the global minimum time in the brachistochronic motion of Chaplygin sleigh
Апстракт
This paper presents a procedure for determining the global minimum
time in the brachistochronic motion of Chaplygin sleigh [3,4] between two specified
positions, with unchanged value of mechanical energy during motion. For this
case, the problem is formulated as the simplest problem of optimal control theory
that is solved by applying Pontryagin’s Maximum Principle [1]. The corresponding
two-point boundary value problem of the system of ordinary nonlinear differential
equations is obtained that is necessary, in a general case, to solve numerically
[2]. The numerical procedure is based on the shooting method, with the
requirement for the assessment of the intervals in which the missing initial
conditions can be found. The assessment is provided of the intervals of initial
values of the conjugate variables, so that the TPBVP solution does not exist for
sure outside those intervals. Graphic representation is given for corresponding
surfaces in 3D space of the missing initial c...onditions, of which each surface
corresponds to satisfying the missing conditions. A number of examples are
provided for multiple solutions of the Maximum Principle, of which the global
minimum is the one corresponding to the minimum time.
Кључне речи:
global minimum time / Chaplygin sleigh / Brachistochrone / Pontryagin’s maximum principleИзвор:
Proceeding of 11th International Symposium on Stability, Vibration, and Control of Machines and Structures, Belgrade, Srbija, 3. - 5. Jul, 2014, 2014, 212-223Издавач:
- Institute of Structronics
- Institute Mihailo Pupin
Финансирање / пројекти:
- Одрживост и унапређење машинских система у енергетици и транспорту применом форензичког инжењерства, еко и робуст дизајна (RS-MESTD-Technological Development (TD or TR)-35006)
- Динамика хибридних система сложених структура. Механика материјала (RS-MESTD-Basic Research (BR or ON)-174001)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Obradović, Aleksandar AU - Radulović, Radoslav PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4037 AB - This paper presents a procedure for determining the global minimum time in the brachistochronic motion of Chaplygin sleigh [3,4] between two specified positions, with unchanged value of mechanical energy during motion. For this case, the problem is formulated as the simplest problem of optimal control theory that is solved by applying Pontryagin’s Maximum Principle [1]. The corresponding two-point boundary value problem of the system of ordinary nonlinear differential equations is obtained that is necessary, in a general case, to solve numerically [2]. The numerical procedure is based on the shooting method, with the requirement for the assessment of the intervals in which the missing initial conditions can be found. The assessment is provided of the intervals of initial values of the conjugate variables, so that the TPBVP solution does not exist for sure outside those intervals. Graphic representation is given for corresponding surfaces in 3D space of the missing initial conditions, of which each surface corresponds to satisfying the missing conditions. A number of examples are provided for multiple solutions of the Maximum Principle, of which the global minimum is the one corresponding to the minimum time. PB - Institute of Structronics PB - Institute Mihailo Pupin C3 - Proceeding of 11th International Symposium on Stability, Vibration, and Control of Machines and Structures, Belgrade, Srbija, 3. - 5. Jul, 2014 T1 - On the global minimum time in the brachistochronic motion of Chaplygin sleigh EP - 223 SP - 212 UR - https://hdl.handle.net/21.15107/rcub_machinery_4037 ER -
@conference{ author = "Obradović, Aleksandar and Radulović, Radoslav", year = "2014", abstract = "This paper presents a procedure for determining the global minimum time in the brachistochronic motion of Chaplygin sleigh [3,4] between two specified positions, with unchanged value of mechanical energy during motion. For this case, the problem is formulated as the simplest problem of optimal control theory that is solved by applying Pontryagin’s Maximum Principle [1]. The corresponding two-point boundary value problem of the system of ordinary nonlinear differential equations is obtained that is necessary, in a general case, to solve numerically [2]. The numerical procedure is based on the shooting method, with the requirement for the assessment of the intervals in which the missing initial conditions can be found. The assessment is provided of the intervals of initial values of the conjugate variables, so that the TPBVP solution does not exist for sure outside those intervals. Graphic representation is given for corresponding surfaces in 3D space of the missing initial conditions, of which each surface corresponds to satisfying the missing conditions. A number of examples are provided for multiple solutions of the Maximum Principle, of which the global minimum is the one corresponding to the minimum time.", publisher = "Institute of Structronics, Institute Mihailo Pupin", journal = "Proceeding of 11th International Symposium on Stability, Vibration, and Control of Machines and Structures, Belgrade, Srbija, 3. - 5. Jul, 2014", title = "On the global minimum time in the brachistochronic motion of Chaplygin sleigh", pages = "223-212", url = "https://hdl.handle.net/21.15107/rcub_machinery_4037" }
Obradović, A.,& Radulović, R.. (2014). On the global minimum time in the brachistochronic motion of Chaplygin sleigh. in Proceeding of 11th International Symposium on Stability, Vibration, and Control of Machines and Structures, Belgrade, Srbija, 3. - 5. Jul, 2014 Institute of Structronics., 212-223. https://hdl.handle.net/21.15107/rcub_machinery_4037
Obradović A, Radulović R. On the global minimum time in the brachistochronic motion of Chaplygin sleigh. in Proceeding of 11th International Symposium on Stability, Vibration, and Control of Machines and Structures, Belgrade, Srbija, 3. - 5. Jul, 2014. 2014;:212-223. https://hdl.handle.net/21.15107/rcub_machinery_4037 .
Obradović, Aleksandar, Radulović, Radoslav, "On the global minimum time in the brachistochronic motion of Chaplygin sleigh" in Proceeding of 11th International Symposium on Stability, Vibration, and Control of Machines and Structures, Belgrade, Srbija, 3. - 5. Jul, 2014 (2014):212-223, https://hdl.handle.net/21.15107/rcub_machinery_4037 .