Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system
Апстракт
The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] 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 [5]. 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]. 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. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined.
Кључне речи:
Variable mass / Pontryagin's maximum principle / Optimal control / Nonholonomic system / brachistochroneИзвор:
Theoretical and Applied Mechanics, 2016, 43, 1, 19-32Издавач:
- Srpsko društvo za mehaniku, Beograd
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Jeremić, Bojan AU - Radulović, Radoslav AU - Obradović, Aleksandar PY - 2016 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2330 AB - The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] 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 [5]. 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]. 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. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined. PB - Srpsko društvo za mehaniku, Beograd T2 - Theoretical and Applied Mechanics T1 - Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system EP - 32 IS - 1 SP - 19 VL - 43 DO - 10.2298/TAM150723002J ER -
@article{ author = "Jeremić, Bojan and Radulović, Radoslav and Obradović, Aleksandar", year = "2016", abstract = "The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] 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 [5]. 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]. 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. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined.", publisher = "Srpsko društvo za mehaniku, Beograd", journal = "Theoretical and Applied Mechanics", title = "Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system", pages = "32-19", number = "1", volume = "43", doi = "10.2298/TAM150723002J" }
Jeremić, B., Radulović, R.,& Obradović, A.. (2016). Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system. in Theoretical and Applied Mechanics Srpsko društvo za mehaniku, Beograd., 43(1), 19-32. https://doi.org/10.2298/TAM150723002J
Jeremić B, Radulović R, Obradović A. Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system. in Theoretical and Applied Mechanics. 2016;43(1):19-32. doi:10.2298/TAM150723002J .
Jeremić, Bojan, Radulović, Radoslav, Obradović, Aleksandar, "Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system" in Theoretical and Applied Mechanics, 43, no. 1 (2016):19-32, https://doi.org/10.2298/TAM150723002J . .