BEHAVIOUR, EXAMINATION AND STABILITY OF THE CONSTRAINED MECHANICAL SYSTEM DESCRIBED WITH NONLINEAR EQUATIONS
Апстракт
The paper considers motion and stability of a holonomic mechanical system in the vertical
plane of an arbitrary force field. Differential equations of motion are created for a given system on
the basis of general theorems of dynamics. Insights into generalized coordinates, Lagrange’s
equations of the second kind, covariant and Hamilton’s equations are presented. Additionally to
numerical procedures in the paper, a review of the theoretical foundations is performed. Also, the
conditions of static equilibrium are solved numerically and by applying the intersection of the two
curves. The paper introduced kinetic as well as the potential energy of the system. The spatial
arrangement of equilibrium positions and behavior of the potential energy in the environment of
the equilibrium positions is shown. Finally, the stability of motion for analysis is approached
through Lagrange - Dirichlet theorem. Moreover, special attention is paid to examining effects
responses of the ...disturbed and undisturbed system. Nonlinear and linearized equations are obtained in order to check the stability of the system for disturbed and undisturbed motion using Hurwitz stability criterion. Various procedures are verificated by drawing the same conclusions.
Кључне речи:
holonomic system / applied mechanics / system stability / nonlinear systems / disturbed motion analysisИзвор:
8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021, 2021, Session M.5.2: General Mechanics (part II) pp. 54-63Издавач:
- Belgrade : Serbian Society of Mechanics
Финансирање / пројекти:
- Министарство науке, технолошког развоја и иновација Републике Србије, институционално финансирање - 200105 (Универзитет у Београду, Машински факултет) (RS-MESTD-inst-2020-200105)
- Динамика хибридних система сложених структура. Механика материјала (RS-MESTD-Basic Research (BR or ON)-174001)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Vesović, Mitra AU - Radulović, Radoslav PY - 2021 UR - https://machinery.mas.bg.ac.rs/handle/123456789/4542 AB - The paper considers motion and stability of a holonomic mechanical system in the vertical plane of an arbitrary force field. Differential equations of motion are created for a given system on the basis of general theorems of dynamics. Insights into generalized coordinates, Lagrange’s equations of the second kind, covariant and Hamilton’s equations are presented. Additionally to numerical procedures in the paper, a review of the theoretical foundations is performed. Also, the conditions of static equilibrium are solved numerically and by applying the intersection of the two curves. The paper introduced kinetic as well as the potential energy of the system. The spatial arrangement of equilibrium positions and behavior of the potential energy in the environment of the equilibrium positions is shown. Finally, the stability of motion for analysis is approached through Lagrange - Dirichlet theorem. Moreover, special attention is paid to examining effects responses of the disturbed and undisturbed system. Nonlinear and linearized equations are obtained in order to check the stability of the system for disturbed and undisturbed motion using Hurwitz stability criterion. Various procedures are verificated by drawing the same conclusions. PB - Belgrade : Serbian Society of Mechanics C3 - 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021 T1 - BEHAVIOUR, EXAMINATION AND STABILITY OF THE CONSTRAINED MECHANICAL SYSTEM DESCRIBED WITH NONLINEAR EQUATIONS EP - 63 SP - Session M.5.2: General Mechanics (part II) pp. 54 UR - https://hdl.handle.net/21.15107/rcub_machinery_4542 ER -
@conference{ author = "Vesović, Mitra and Radulović, Radoslav", year = "2021", abstract = "The paper considers motion and stability of a holonomic mechanical system in the vertical plane of an arbitrary force field. Differential equations of motion are created for a given system on the basis of general theorems of dynamics. Insights into generalized coordinates, Lagrange’s equations of the second kind, covariant and Hamilton’s equations are presented. Additionally to numerical procedures in the paper, a review of the theoretical foundations is performed. Also, the conditions of static equilibrium are solved numerically and by applying the intersection of the two curves. The paper introduced kinetic as well as the potential energy of the system. The spatial arrangement of equilibrium positions and behavior of the potential energy in the environment of the equilibrium positions is shown. Finally, the stability of motion for analysis is approached through Lagrange - Dirichlet theorem. Moreover, special attention is paid to examining effects responses of the disturbed and undisturbed system. Nonlinear and linearized equations are obtained in order to check the stability of the system for disturbed and undisturbed motion using Hurwitz stability criterion. Various procedures are verificated by drawing the same conclusions.", publisher = "Belgrade : Serbian Society of Mechanics", journal = "8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021", title = "BEHAVIOUR, EXAMINATION AND STABILITY OF THE CONSTRAINED MECHANICAL SYSTEM DESCRIBED WITH NONLINEAR EQUATIONS", pages = "63-Session M.5.2: General Mechanics (part II) pp. 54", url = "https://hdl.handle.net/21.15107/rcub_machinery_4542" }
Vesović, M.,& Radulović, R.. (2021). BEHAVIOUR, EXAMINATION AND STABILITY OF THE CONSTRAINED MECHANICAL SYSTEM DESCRIBED WITH NONLINEAR EQUATIONS. in 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021 Belgrade : Serbian Society of Mechanics., Session M.5.2: General Mechanics (part II) pp. 54-63. https://hdl.handle.net/21.15107/rcub_machinery_4542
Vesović M, Radulović R. BEHAVIOUR, EXAMINATION AND STABILITY OF THE CONSTRAINED MECHANICAL SYSTEM DESCRIBED WITH NONLINEAR EQUATIONS. in 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021. 2021;:Session M.5.2: General Mechanics (part II) pp. 54-63. https://hdl.handle.net/21.15107/rcub_machinery_4542 .
Vesović, Mitra, Radulović, Radoslav, "BEHAVIOUR, EXAMINATION AND STABILITY OF THE CONSTRAINED MECHANICAL SYSTEM DESCRIBED WITH NONLINEAR EQUATIONS" in 8th International Congress of Serbian Society of Mechanics Kragujevac, Serbia, June 28-30, 2021 (2021):Session M.5.2: General Mechanics (part II) pp. 54-63, https://hdl.handle.net/21.15107/rcub_machinery_4542 .