Global minimum time for the brachistohronic motion of a particle in an arbitrary field of potential forces
Апстракт
The problem of the brachistochronic motion of a particle in space is considered. Particle
М moves in the field of known potential forces. The brachistochrone problem is formulated as an
optimal control task, where the particle velocity projections are taken as control variables. The
problem considered is reduced to solving the corresponding two-point boundary–value problem
(TPBVP).The appropriate numerical procedure to apply in determining the solutions to the
TPBVP is based on the shooting method. The paper presents the procedure for estimating the
interval of initial values of the conjugate vector coordinates. Based on given estimation, it may be
claimed that all solutions to the corresponding TPBVP are certainly located within given
intervals, and thereby the global minimum time too for the brachistochronic motion of a particle.
In the case of multiple solutions of the principle of maximum, the global minimum is the solution
corresponding to the minimum time.
Кључне речи:
Particle / Brachistochronic motion / Optimal control / Pontryagin’s maximum principle, / Global minimum time / Shooting methodИзвор:
Proceeding of 6th International Congress of Serbian Society of Mechanics Mountain Tara, Serbia, June 19-21, 2017, 2017, G2d-Издавач:
- Beograd : Srpsko društvo za mehaniku
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 - Radulović, Radoslav AU - Jeremić, Bojan AU - Obradović, Aleksandar AU - Stokić, Zoran PY - 2017 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4054 AB - The problem of the brachistochronic motion of a particle in space is considered. Particle М moves in the field of known potential forces. The brachistochrone problem is formulated as an optimal control task, where the particle velocity projections are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary–value problem (TPBVP).The appropriate numerical procedure to apply in determining the solutions to the TPBVP is based on the shooting method. The paper presents the procedure for estimating the interval of initial values of the conjugate vector coordinates. Based on given estimation, it may be claimed that all solutions to the corresponding TPBVP are certainly located within given intervals, and thereby the global minimum time too for the brachistochronic motion of a particle. In the case of multiple solutions of the principle of maximum, the global minimum is the solution corresponding to the minimum time. PB - Beograd : Srpsko društvo za mehaniku C3 - Proceeding of 6th International Congress of Serbian Society of Mechanics Mountain Tara, Serbia, June 19-21, 2017 T1 - Global minimum time for the brachistohronic motion of a particle in an arbitrary field of potential forces SP - G2d UR - https://hdl.handle.net/21.15107/rcub_machinery_4054 ER -
@conference{ author = "Radulović, Radoslav and Jeremić, Bojan and Obradović, Aleksandar and Stokić, Zoran", year = "2017", abstract = "The problem of the brachistochronic motion of a particle in space is considered. Particle М moves in the field of known potential forces. The brachistochrone problem is formulated as an optimal control task, where the particle velocity projections are taken as control variables. The problem considered is reduced to solving the corresponding two-point boundary–value problem (TPBVP).The appropriate numerical procedure to apply in determining the solutions to the TPBVP is based on the shooting method. The paper presents the procedure for estimating the interval of initial values of the conjugate vector coordinates. Based on given estimation, it may be claimed that all solutions to the corresponding TPBVP are certainly located within given intervals, and thereby the global minimum time too for the brachistochronic motion of a particle. In the case of multiple solutions of the principle of maximum, the global minimum is the solution corresponding to the minimum time.", publisher = "Beograd : Srpsko društvo za mehaniku", journal = "Proceeding of 6th International Congress of Serbian Society of Mechanics Mountain Tara, Serbia, June 19-21, 2017", title = "Global minimum time for the brachistohronic motion of a particle in an arbitrary field of potential forces", pages = "G2d", url = "https://hdl.handle.net/21.15107/rcub_machinery_4054" }
Radulović, R., Jeremić, B., Obradović, A.,& Stokić, Z.. (2017). Global minimum time for the brachistohronic motion of a particle in an arbitrary field of potential forces. in Proceeding of 6th International Congress of Serbian Society of Mechanics Mountain Tara, Serbia, June 19-21, 2017 Beograd : Srpsko društvo za mehaniku., G2d. https://hdl.handle.net/21.15107/rcub_machinery_4054
Radulović R, Jeremić B, Obradović A, Stokić Z. Global minimum time for the brachistohronic motion of a particle in an arbitrary field of potential forces. in Proceeding of 6th International Congress of Serbian Society of Mechanics Mountain Tara, Serbia, June 19-21, 2017. 2017;:G2d. https://hdl.handle.net/21.15107/rcub_machinery_4054 .
Radulović, Radoslav, Jeremić, Bojan, Obradović, Aleksandar, Stokić, Zoran, "Global minimum time for the brachistohronic motion of a particle in an arbitrary field of potential forces" in Proceeding of 6th International Congress of Serbian Society of Mechanics Mountain Tara, Serbia, June 19-21, 2017 (2017):G2d, https://hdl.handle.net/21.15107/rcub_machinery_4054 .