Modelovanje i analiza stabilnosti datog nelinearnog sistema
Modelling and stability analysis of the nonlinear system
Апстракт
The production industries have repeatedly combated the problem of system modelling. Successful control of a system depends mainly on the exactness of the mathematical model that predicts its dynamic. Different types of studies are very common in the complicated challenges involving the estimations and approximations in describing nonlinear machines are based on a variety of studies. This article examines the behaviour and stability of holonomic mechanical system in the the arbitrary parameter sets and functional configuration of forces. Differential equations of the behaviour are obtained for the proposed system on the ground of general mechanical theorems, kinetic and potential energies of the system. Lagrange’s equations of the first and second kind are introduced, as well as the representation of the system in the generalized coordinates and in Hamilton’s equations. In addition to the numerical calculations applied the system, the theoretical structures and clarifications on which a...ll of the methods rely on are also presented. Furthermore, static equilibriums are found via two different approaches: graphical and numerical. Above all, stability of motion of undisturbed system and, later, the system that works under the action of an external disturbance was inspected. Finally, the stability of motion is reviewed through Lagrange–Dirichlet theorem, and Routh and Hurwitz criteria. Linearized equations are obtained from the nonlinear ones, and previous conclusions for the stability were proved.
Кључне речи:
Stability of undisturbed and disturbed motion / Nonlinear systems / Holonomic system / Hamiltonian function / Applied mechanicsИзвор:
Theoretical and Applied Mechanics, 2022, 49, 1, 29-48Издавач:
- Srpsko društvo za mehaniku, Beograd
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Vesović, Mitra AU - Radulović, Radoslav PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3821 AB - The production industries have repeatedly combated the problem of system modelling. Successful control of a system depends mainly on the exactness of the mathematical model that predicts its dynamic. Different types of studies are very common in the complicated challenges involving the estimations and approximations in describing nonlinear machines are based on a variety of studies. This article examines the behaviour and stability of holonomic mechanical system in the the arbitrary parameter sets and functional configuration of forces. Differential equations of the behaviour are obtained for the proposed system on the ground of general mechanical theorems, kinetic and potential energies of the system. Lagrange’s equations of the first and second kind are introduced, as well as the representation of the system in the generalized coordinates and in Hamilton’s equations. In addition to the numerical calculations applied the system, the theoretical structures and clarifications on which all of the methods rely on are also presented. Furthermore, static equilibriums are found via two different approaches: graphical and numerical. Above all, stability of motion of undisturbed system and, later, the system that works under the action of an external disturbance was inspected. Finally, the stability of motion is reviewed through Lagrange–Dirichlet theorem, and Routh and Hurwitz criteria. Linearized equations are obtained from the nonlinear ones, and previous conclusions for the stability were proved. PB - Srpsko društvo za mehaniku, Beograd T2 - Theoretical and Applied Mechanics T1 - Modelovanje i analiza stabilnosti datog nelinearnog sistema T1 - Modelling and stability analysis of the nonlinear system EP - 48 IS - 1 SP - 29 VL - 49 DO - 10.2298/TAM211101003V ER -
@article{ author = "Vesović, Mitra and Radulović, Radoslav", year = "2022", abstract = "The production industries have repeatedly combated the problem of system modelling. Successful control of a system depends mainly on the exactness of the mathematical model that predicts its dynamic. Different types of studies are very common in the complicated challenges involving the estimations and approximations in describing nonlinear machines are based on a variety of studies. This article examines the behaviour and stability of holonomic mechanical system in the the arbitrary parameter sets and functional configuration of forces. Differential equations of the behaviour are obtained for the proposed system on the ground of general mechanical theorems, kinetic and potential energies of the system. Lagrange’s equations of the first and second kind are introduced, as well as the representation of the system in the generalized coordinates and in Hamilton’s equations. In addition to the numerical calculations applied the system, the theoretical structures and clarifications on which all of the methods rely on are also presented. Furthermore, static equilibriums are found via two different approaches: graphical and numerical. Above all, stability of motion of undisturbed system and, later, the system that works under the action of an external disturbance was inspected. Finally, the stability of motion is reviewed through Lagrange–Dirichlet theorem, and Routh and Hurwitz criteria. Linearized equations are obtained from the nonlinear ones, and previous conclusions for the stability were proved.", publisher = "Srpsko društvo za mehaniku, Beograd", journal = "Theoretical and Applied Mechanics", title = "Modelovanje i analiza stabilnosti datog nelinearnog sistema, Modelling and stability analysis of the nonlinear system", pages = "48-29", number = "1", volume = "49", doi = "10.2298/TAM211101003V" }
Vesović, M.,& Radulović, R.. (2022). Modelovanje i analiza stabilnosti datog nelinearnog sistema. in Theoretical and Applied Mechanics Srpsko društvo za mehaniku, Beograd., 49(1), 29-48. https://doi.org/10.2298/TAM211101003V
Vesović M, Radulović R. Modelovanje i analiza stabilnosti datog nelinearnog sistema. in Theoretical and Applied Mechanics. 2022;49(1):29-48. doi:10.2298/TAM211101003V .
Vesović, Mitra, Radulović, Radoslav, "Modelovanje i analiza stabilnosti datog nelinearnog sistema" in Theoretical and Applied Mechanics, 49, no. 1 (2022):29-48, https://doi.org/10.2298/TAM211101003V . .