Realization of the brachistohronic motion of a nonholonomic variable mass mechanical system by ideal holonomic constraint
Abstract
The paper considers realization of the brachistochronic motion of a nonholonomic
mechanical system, composed of variable mass particles, by means of an ideal holonomic
constraint. It is assumed that the system performs planar motion in an arbitrary field of forces
and that it has two degrees of freedom. In addition, the laws of the time-rate of mass variation of
the particles, as well as relative velocities of the expelled and gained particles, respectively, are
known. The first time-derivative of quasi-velocity is taken as control variable. 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.
Keywords:
brachistochrone / variable mass / mechanical system / nonholonomic constraints / holonomic constraints / Pontryagin’s maximum principle / optimal controlSource:
Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019, 2019, M1i-Publisher:
- Srpsko društvo za mehaniku
Funding / projects:
- Dynamics of hybrid systems with complex structures. Mechanics of materials. (RS-MESTD-Basic Research (BR or ON)-174001)
- 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)
Collections
Institution/Community
Mašinski fakultetTY - CONF AU - Radulović, Radoslav AU - Jeremić, Bojan AU - Obradović, Aleksandar PY - 2019 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4034 AB - The paper considers realization of the brachistochronic motion of a nonholonomic mechanical system, composed of variable mass particles, by means of an ideal holonomic constraint. It is assumed that the system performs planar motion in an arbitrary field of forces and that it has two degrees of freedom. In addition, the laws of the time-rate of mass variation of the particles, as well as relative velocities of the expelled and gained particles, respectively, are known. The first time-derivative of quasi-velocity is taken as control variable. 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. PB - Srpsko društvo za mehaniku C3 - Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 T1 - Realization of the brachistohronic motion of a nonholonomic variable mass mechanical system by ideal holonomic constraint SP - M1i UR - https://hdl.handle.net/21.15107/rcub_machinery_4034 ER -
@conference{ author = "Radulović, Radoslav and Jeremić, Bojan and Obradović, Aleksandar", year = "2019", abstract = "The paper considers realization of the brachistochronic motion of a nonholonomic mechanical system, composed of variable mass particles, by means of an ideal holonomic constraint. It is assumed that the system performs planar motion in an arbitrary field of forces and that it has two degrees of freedom. In addition, the laws of the time-rate of mass variation of the particles, as well as relative velocities of the expelled and gained particles, respectively, are known. The first time-derivative of quasi-velocity is taken as control variable. 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.", publisher = "Srpsko društvo za mehaniku", journal = "Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019", title = "Realization of the brachistohronic motion of a nonholonomic variable mass mechanical system by ideal holonomic constraint", pages = "M1i", url = "https://hdl.handle.net/21.15107/rcub_machinery_4034" }
Radulović, R., Jeremić, B.,& Obradović, A.. (2019). Realization of the brachistohronic motion of a nonholonomic variable mass mechanical system by ideal holonomic constraint. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 Srpsko društvo za mehaniku., M1i. https://hdl.handle.net/21.15107/rcub_machinery_4034
Radulović R, Jeremić B, Obradović A. Realization of the brachistohronic motion of a nonholonomic variable mass mechanical system by ideal holonomic constraint. in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019. 2019;:M1i. https://hdl.handle.net/21.15107/rcub_machinery_4034 .
Radulović, Radoslav, Jeremić, Bojan, Obradović, Aleksandar, "Realization of the brachistohronic motion of a nonholonomic variable mass mechanical system by ideal holonomic constraint" in Proceeding of 7th International Congress of Serbian Society of Mechanics Sremski Karlovci, Serbia, June 24-26, 2019 (2019):M1i, https://hdl.handle.net/21.15107/rcub_machinery_4034 .