Brachistohronic motion of a variable mass nonholonomic mechanical system
Апстракт
The paper considers the brachistochronic motion of a variable mass nonholonomic
mechanical system [4] in a horizontal plane, between two specified positions. Variable mass
particles are interconnected by a lightweight mechanism of the ’pitchfork’ type. The law of the
time-rate of mass variation of the particles, as well as relative velocities of the expelled particles,
as a function of time, are known. Differential equations of motion, where the reactions of
nonholonomic constraints and control forces figure, are created based on the general theorems of
dynamics of a variable mass mechanical system [6]. The formulated brachistochrone problem,
with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal
control by applying Pontryagin’s maximum principle [1]. A corresponding two-point boundary
value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained,
which, in a general case, has to be numerically solve...d [2]. Numerical procedure for solving the
TPBVP is performed by the shooting method. On the basis of thus obtained brachistochronic
motion, the active control forces, along with the reactions of nonholonomic constraints, are
determined. The analysis of the brachistochronic motion for different values of the initial position
of a variable mass particle B is presented.
Кључне речи:
Brachistochrone / variable mass / nonholonomic system / Pontryagin’s maximum principle, / optimal controlИзвор:
Proceeding of 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015, 2015, G3e-Издавач:
- Srpsko društvo za mehaniku
Финансирање / пројекти:
- Динамика хибридних система сложених структура. Механика материјала (RS-MESTD-Basic Research (BR or ON)-174001)
- Одрживост и унапређење машинских система у енергетици и транспорту применом форензичког инжењерства, еко и робуст дизајна (RS-MESTD-Technological Development (TD or TR)-35006)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Jeremić, Bojan AU - Radulović, Radoslav AU - Obradović, Aleksandar PY - 2015 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4055 AB - The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [4] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ’pitchfork’ type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [6]. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin’s maximum principle [1]. A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2]. Numerical procedure for solving the TPBVP is performed by the shooting method. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined. The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle B is presented. PB - Srpsko društvo za mehaniku C3 - Proceeding of 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015 T1 - Brachistohronic motion of a variable mass nonholonomic mechanical system SP - G3e UR - https://hdl.handle.net/21.15107/rcub_machinery_4055 ER -
@conference{ author = "Jeremić, Bojan and Radulović, Radoslav and Obradović, Aleksandar", year = "2015", abstract = "The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [4] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ’pitchfork’ type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [6]. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin’s maximum principle [1]. A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2]. Numerical procedure for solving the TPBVP is performed by the shooting method. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined. The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle B is presented.", publisher = "Srpsko društvo za mehaniku", journal = "Proceeding of 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015", title = "Brachistohronic motion of a variable mass nonholonomic mechanical system", pages = "G3e", url = "https://hdl.handle.net/21.15107/rcub_machinery_4055" }
Jeremić, B., Radulović, R.,& Obradović, A.. (2015). Brachistohronic motion of a variable mass nonholonomic mechanical system. in Proceeding of 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015 Srpsko društvo za mehaniku., G3e. https://hdl.handle.net/21.15107/rcub_machinery_4055
Jeremić B, Radulović R, Obradović A. Brachistohronic motion of a variable mass nonholonomic mechanical system. in Proceeding of 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015. 2015;:G3e. https://hdl.handle.net/21.15107/rcub_machinery_4055 .
Jeremić, Bojan, Radulović, Radoslav, Obradović, Aleksandar, "Brachistohronic motion of a variable mass nonholonomic mechanical system" in Proceeding of 5th International Congress of Serbian Society of Mechanics Arandjelovac, Serbia, June 15-17, 2015 (2015):G3e, https://hdl.handle.net/21.15107/rcub_machinery_4055 .