Realizing brachistohronic motion of a variable mass body by centrodes
Abstract
The paper considers realization of the brachistochronic motion of a mechanical system,
composed of free body and variable mass material points, by means of an ideal constraint in the
form of the centrodes. It is assumed that the system performs planar motion in an arbitrary field
of forces and that it has three degrees of freedom. In addition, the laws of the time-rate of mass
variation of the material points, as well as relative velocities of the expelled particles,
respectively, are known. Constraint reactions of the centrodes are expressed in the function of the
generalized forces. Applying Pontryagin's maximum principle and singular optimal control
theory, the problem of brachistochronic motion is solved as a two-point boundary value problem
(TPBVP). The considerations are illustrated via an example, where it is examined how the change
in the initial energy of the system affects the normal reaction of the connection and thus the
coefficient of rolling friction.
Keywords:
brachistochrone / variable mass / mechanical system / Pontryagin’s maximum principle / optimal controlSource:
Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019, 2019, G3a-Publisher:
- Srpsko društvo za mehaniku
Funding / projects:
- Sustainability and improvement of mechanical systems in energetic, material handling and conveying by using forensic engineering, environmental and robust design (RS-MESTD-Technological Development (TD or TR)-35006)
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Jeremić, Bojan AU - Radulović, Radoslav AU - Obradović, Aleksandar PY - 2019 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4033 AB - The paper considers realization of the brachistochronic motion of a mechanical system, composed of free body and variable mass material points, by means of an ideal constraint in the form of the centrodes. It is assumed that the system performs planar motion in an arbitrary field of forces and that it has three degrees of freedom. In addition, the laws of the time-rate of mass variation of the material points, as well as relative velocities of the expelled particles, respectively, are known. Constraint reactions of the centrodes are expressed in the function of the generalized forces. Applying Pontryagin's maximum principle and singular optimal control theory, the problem of brachistochronic motion is solved as a two-point boundary value problem (TPBVP). The considerations are illustrated via an example, where it is examined how the change in the initial energy of the system affects the normal reaction of the connection and thus the coefficient of rolling friction. PB - Srpsko društvo za mehaniku C3 - Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 T1 - Realizing brachistohronic motion of a variable mass body by centrodes SP - G3a UR - https://hdl.handle.net/21.15107/rcub_machinery_4033 ER -
@conference{ author = "Jeremić, Bojan and Radulović, Radoslav and Obradović, Aleksandar", year = "2019", abstract = "The paper considers realization of the brachistochronic motion of a mechanical system, composed of free body and variable mass material points, by means of an ideal constraint in the form of the centrodes. It is assumed that the system performs planar motion in an arbitrary field of forces and that it has three degrees of freedom. In addition, the laws of the time-rate of mass variation of the material points, as well as relative velocities of the expelled particles, respectively, are known. Constraint reactions of the centrodes are expressed in the function of the generalized forces. Applying Pontryagin's maximum principle and singular optimal control theory, the problem of brachistochronic motion is solved as a two-point boundary value problem (TPBVP). The considerations are illustrated via an example, where it is examined how the change in the initial energy of the system affects the normal reaction of the connection and thus the coefficient of rolling friction.", publisher = "Srpsko društvo za mehaniku", journal = "Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019", title = "Realizing brachistohronic motion of a variable mass body by centrodes", pages = "G3a", url = "https://hdl.handle.net/21.15107/rcub_machinery_4033" }
Jeremić, B., Radulović, R.,& Obradović, A.. (2019). Realizing brachistohronic motion of a variable mass body by centrodes. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 Srpsko društvo za mehaniku., G3a. https://hdl.handle.net/21.15107/rcub_machinery_4033
Jeremić B, Radulović R, Obradović A. Realizing brachistohronic motion of a variable mass body by centrodes. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019. 2019;:G3a. https://hdl.handle.net/21.15107/rcub_machinery_4033 .
Jeremić, Bojan, Radulović, Radoslav, Obradović, Aleksandar, "Realizing brachistohronic motion of a variable mass body by centrodes" in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 (2019):G3a, https://hdl.handle.net/21.15107/rcub_machinery_4033 .