On the stability of equilibria of nonholonomic systems with nonlinear constraints
Samo za registrovane korisnike
2010
Članak u časopisu (Objavljena verzija)
Metapodaci
Prikaz svih podataka o dokumentuApstrakt
Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechanical systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The motion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three cases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlinear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints.
Ključne reči:
nonholonomic system / Lyapunov first method / instability of equilibriumIzvor:
Applied Mathematics and Mechanics-English Edition, 2010, 31, 6, 751-760Izdavač:
- SHANGHAI UNIV, SHANGHAI
Finansiranje / projekti:
- Savremeni problemi mehanike deformabilnog tela (RS-MESTD-MPN2006-2010-144019)
- Razvoj bioloških motivisanih kontrolnih i senzorskih sistema i izrada studijskog prototipa nožnog pomagala (RS-MESTD-MPN2006-2010-20152)
- Razvoj mašina visokih performansi i metoda za identifikaciju njihovog odziva na unutrašnje i spoljašnje poremećaje (RS-MESTD-MPN2006-2010-14052)
DOI: 10.1007/s10483-010-1309-7
ISSN: 0253-4827
WoS: 000278572100009
Scopus: 2-s2.0-77954884207
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Cović, V. AU - Vesković, M. AU - Djurić, D. AU - Obradović, Aleksandar PY - 2010 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1076 AB - Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechanical systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The motion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three cases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlinear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints. PB - SHANGHAI UNIV, SHANGHAI T2 - Applied Mathematics and Mechanics-English Edition T1 - On the stability of equilibria of nonholonomic systems with nonlinear constraints EP - 760 IS - 6 SP - 751 VL - 31 DO - 10.1007/s10483-010-1309-7 ER -
@article{ author = "Cović, V. and Vesković, M. and Djurić, D. and Obradović, Aleksandar", year = "2010", abstract = "Lyapunov's first method, extended by V. V. Kozlov to nonlinear mechanical systems, is applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The motion of the system is limited by ideal nonlinear nonholonomic constraints. Five cases determined by the relationship between the degree of the first nontrivial polynomials in Maclaurin's series for the potential energy and the functions that can be generated from the equations of nonlinear nonholonomic constraints are analyzed. In the three cases, the theorem on the instability of the position of equilibrium of nonholonomic systems with linear homogeneous constraints (V. V. Kozlov (1986)) is generalized to the case of nonlinear nonhomogeneous constraints. In the other two cases, new theorems are set extending the result from V. V. Kozlov (1994) to nonholonomic systems with nonlinear constraints.", publisher = "SHANGHAI UNIV, SHANGHAI", journal = "Applied Mathematics and Mechanics-English Edition", title = "On the stability of equilibria of nonholonomic systems with nonlinear constraints", pages = "760-751", number = "6", volume = "31", doi = "10.1007/s10483-010-1309-7" }
Cović, V., Vesković, M., Djurić, D.,& Obradović, A.. (2010). On the stability of equilibria of nonholonomic systems with nonlinear constraints. in Applied Mathematics and Mechanics-English Edition SHANGHAI UNIV, SHANGHAI., 31(6), 751-760. https://doi.org/10.1007/s10483-010-1309-7
Cović V, Vesković M, Djurić D, Obradović A. On the stability of equilibria of nonholonomic systems with nonlinear constraints. in Applied Mathematics and Mechanics-English Edition. 2010;31(6):751-760. doi:10.1007/s10483-010-1309-7 .
Cović, V., Vesković, M., Djurić, D., Obradović, Aleksandar, "On the stability of equilibria of nonholonomic systems with nonlinear constraints" in Applied Mathematics and Mechanics-English Edition, 31, no. 6 (2010):751-760, https://doi.org/10.1007/s10483-010-1309-7 . .