Brachistochronic motion of a variable mass system
Апстракт
A mechanical system consisting of rigid bodies and material particles, of which
some particles are with variable masses, is considered. Laws of variation of the masses of
the points and relative velocity of particles separating from the points are well-known. The
system is moving in an arbitrary field of known potential and nonpotential forces. Applying
Pontryagin’s Maximum Principle and singular optimal control theory, brachistochronic
motion is determined. A two-point boundary value problem, due to nonlinearity of equations
in a general case, is needed to be solved using some of the numerical procedures. Here the
Shooting method is used, where the missing boundary conditions are chosen so as to be the
physical variables (velocity and mass). The field where they are found can be approximately
estimated, which is not the case with the conjugate vector coordinates being of purely
mathematical nature. The paper also presents the manner of brachistrochronic motion
realization w...ithout the action of active control forces. It is realized by subsequent imposition
to the system a corresponding number of independent ideal holonomic mechanical
constraints. The constraints must be in accordance with the previously determined
brachistochronic motion of the system. The method is illustrated by an example of
determining the brachistochronic motion of the system with three degrees of freedom and
method of its realization. The system consists of one rigid body to which two points of
variable masses are attached, where the system is moving in a vertical plane.
Brachistochronic motion is realized by the help of two ideal holonomic constraints.
Извор:
Proceedings of IConSSM 2011, The 3rd International Congress of Serbian Society of Mechanics, Vlasina Lake, Serbia, Serbian Society for Mechanics,Србија, 5. - 8. Jul, 2011, 2011, 1237-1246Издавач:
- 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)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Obradović, Aleksandar AU - Šalinić, Slaviša AU - Jeremić, Olivera AU - Mitrović, Zoran PY - 2011 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3993 AB - A mechanical system consisting of rigid bodies and material particles, of which some particles are with variable masses, is considered. Laws of variation of the masses of the points and relative velocity of particles separating from the points are well-known. The system is moving in an arbitrary field of known potential and nonpotential forces. Applying Pontryagin’s Maximum Principle and singular optimal control theory, brachistochronic motion is determined. A two-point boundary value problem, due to nonlinearity of equations in a general case, is needed to be solved using some of the numerical procedures. Here the Shooting method is used, where the missing boundary conditions are chosen so as to be the physical variables (velocity and mass). The field where they are found can be approximately estimated, which is not the case with the conjugate vector coordinates being of purely mathematical nature. The paper also presents the manner of brachistrochronic motion realization without the action of active control forces. It is realized by subsequent imposition to the system a corresponding number of independent ideal holonomic mechanical constraints. The constraints must be in accordance with the previously determined brachistochronic motion of the system. The method is illustrated by an example of determining the brachistochronic motion of the system with three degrees of freedom and method of its realization. The system consists of one rigid body to which two points of variable masses are attached, where the system is moving in a vertical plane. Brachistochronic motion is realized by the help of two ideal holonomic constraints. PB - Beograd : Srpsko društvo za mehaniku C3 - Proceedings of IConSSM 2011, The 3rd International Congress of Serbian Society of Mechanics, Vlasina Lake, Serbia, Serbian Society for Mechanics,Србија, 5. - 8. Jul, 2011 T1 - Brachistochronic motion of a variable mass system EP - 1246 SP - 1237 UR - https://hdl.handle.net/21.15107/rcub_machinery_3993 ER -
@conference{ author = "Obradović, Aleksandar and Šalinić, Slaviša and Jeremić, Olivera and Mitrović, Zoran", year = "2011", abstract = "A mechanical system consisting of rigid bodies and material particles, of which some particles are with variable masses, is considered. Laws of variation of the masses of the points and relative velocity of particles separating from the points are well-known. The system is moving in an arbitrary field of known potential and nonpotential forces. Applying Pontryagin’s Maximum Principle and singular optimal control theory, brachistochronic motion is determined. A two-point boundary value problem, due to nonlinearity of equations in a general case, is needed to be solved using some of the numerical procedures. Here the Shooting method is used, where the missing boundary conditions are chosen so as to be the physical variables (velocity and mass). The field where they are found can be approximately estimated, which is not the case with the conjugate vector coordinates being of purely mathematical nature. The paper also presents the manner of brachistrochronic motion realization without the action of active control forces. It is realized by subsequent imposition to the system a corresponding number of independent ideal holonomic mechanical constraints. The constraints must be in accordance with the previously determined brachistochronic motion of the system. The method is illustrated by an example of determining the brachistochronic motion of the system with three degrees of freedom and method of its realization. The system consists of one rigid body to which two points of variable masses are attached, where the system is moving in a vertical plane. Brachistochronic motion is realized by the help of two ideal holonomic constraints.", publisher = "Beograd : Srpsko društvo za mehaniku", journal = "Proceedings of IConSSM 2011, The 3rd International Congress of Serbian Society of Mechanics, Vlasina Lake, Serbia, Serbian Society for Mechanics,Србија, 5. - 8. Jul, 2011", title = "Brachistochronic motion of a variable mass system", pages = "1246-1237", url = "https://hdl.handle.net/21.15107/rcub_machinery_3993" }
Obradović, A., Šalinić, S., Jeremić, O.,& Mitrović, Z.. (2011). Brachistochronic motion of a variable mass system. in Proceedings of IConSSM 2011, The 3rd International Congress of Serbian Society of Mechanics, Vlasina Lake, Serbia, Serbian Society for Mechanics,Србија, 5. - 8. Jul, 2011 Beograd : Srpsko društvo za mehaniku., 1237-1246. https://hdl.handle.net/21.15107/rcub_machinery_3993
Obradović A, Šalinić S, Jeremić O, Mitrović Z. Brachistochronic motion of a variable mass system. in Proceedings of IConSSM 2011, The 3rd International Congress of Serbian Society of Mechanics, Vlasina Lake, Serbia, Serbian Society for Mechanics,Србија, 5. - 8. Jul, 2011. 2011;:1237-1246. https://hdl.handle.net/21.15107/rcub_machinery_3993 .
Obradović, Aleksandar, Šalinić, Slaviša, Jeremić, Olivera, Mitrović, Zoran, "Brachistochronic motion of a variable mass system" in Proceedings of IConSSM 2011, The 3rd International Congress of Serbian Society of Mechanics, Vlasina Lake, Serbia, Serbian Society for Mechanics,Србија, 5. - 8. Jul, 2011 (2011):1237-1246, https://hdl.handle.net/21.15107/rcub_machinery_3993 .