Realizing Brachistochronic Planar Motion of a Variable Mass Nonholonomic Mechanical System by an Ideal Holonomic Constraint with Restricted Reaction
Apstrakt
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 with restricted reaction. 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. Restricted reaction of the holonomic constraint is taken for the scalar control. 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). Since the reaction of the constraint is restricted, different types of control structures are examined, from singular to totally nonsingular. The considerations are illustrated via an example.
Ključne reči:
variable mass / restricted reactions / Pontryagin's maximum principle / optimal control / nonholonomic constraints / mechanical system / holonomic constraints / BrachistochroneIzvor:
Filomat, 2019, 33, 14, 4387-4401Izdavač:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Finansiranje / projekti:
- Dinamika hibridnih sistema složenih struktura. Mehanika materijala (RS-MESTD-Basic Research (BR or ON)-174001)
- Održivost i unapređenje mašinskih sistema u energetici i transportu primenom forenzičkog inženjerstva, eko i robust dizajna (RS-MESTD-Technological Development (TD or TR)-35006)
DOI: 10.2298/FIL1914387J
ISSN: 0354-5180
WoS: 000502089300005
Scopus: 2-s2.0-85078282257
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Jeremić, Bojan AU - Radulović, Radoslav AU - Zorić, Nemanja AU - Dražić, Milan PY - 2019 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2997 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 with restricted reaction. 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. Restricted reaction of the holonomic constraint is taken for the scalar control. 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). Since the reaction of the constraint is restricted, different types of control structures are examined, from singular to totally nonsingular. The considerations are illustrated via an example. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - Realizing Brachistochronic Planar Motion of a Variable Mass Nonholonomic Mechanical System by an Ideal Holonomic Constraint with Restricted Reaction EP - 4401 IS - 14 SP - 4387 VL - 33 DO - 10.2298/FIL1914387J ER -
@article{ author = "Jeremić, Bojan and Radulović, Radoslav and Zorić, Nemanja and Dražić, Milan", 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 with restricted reaction. 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. Restricted reaction of the holonomic constraint is taken for the scalar control. 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). Since the reaction of the constraint is restricted, different types of control structures are examined, from singular to totally nonsingular. The considerations are illustrated via an example.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "Realizing Brachistochronic Planar Motion of a Variable Mass Nonholonomic Mechanical System by an Ideal Holonomic Constraint with Restricted Reaction", pages = "4401-4387", number = "14", volume = "33", doi = "10.2298/FIL1914387J" }
Jeremić, B., Radulović, R., Zorić, N.,& Dražić, M.. (2019). Realizing Brachistochronic Planar Motion of a Variable Mass Nonholonomic Mechanical System by an Ideal Holonomic Constraint with Restricted Reaction. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 33(14), 4387-4401. https://doi.org/10.2298/FIL1914387J
Jeremić B, Radulović R, Zorić N, Dražić M. Realizing Brachistochronic Planar Motion of a Variable Mass Nonholonomic Mechanical System by an Ideal Holonomic Constraint with Restricted Reaction. in Filomat. 2019;33(14):4387-4401. doi:10.2298/FIL1914387J .
Jeremić, Bojan, Radulović, Radoslav, Zorić, Nemanja, Dražić, Milan, "Realizing Brachistochronic Planar Motion of a Variable Mass Nonholonomic Mechanical System by an Ideal Holonomic Constraint with Restricted Reaction" in Filomat, 33, no. 14 (2019):4387-4401, https://doi.org/10.2298/FIL1914387J . .