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The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom. / Bibikov, Yu N.

в: Journal of Applied Mathematics and Mechanics, Том 77, № 2, 2013, стр. 167-171.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Bibikov, YN 2013, 'The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom', Journal of Applied Mathematics and Mechanics, Том. 77, № 2, стр. 167-171. https://doi.org/10.1016/j.jappmathmech.2013.07.006

APA

Bibikov, Y. N. (2013). The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom. Journal of Applied Mathematics and Mechanics, 77(2), 167-171. https://doi.org/10.1016/j.jappmathmech.2013.07.006

Vancouver

Bibikov YN. The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom. Journal of Applied Mathematics and Mechanics. 2013;77(2):167-171. https://doi.org/10.1016/j.jappmathmech.2013.07.006

Author

Bibikov, Yu N. / The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom. в: Journal of Applied Mathematics and Mechanics. 2013 ; Том 77, № 2. стр. 167-171.

BibTeX

@article{30f17cfb5ba74fb18ec2490dfb1c7055,
title = "The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom",
abstract = "The stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom with a Hamiltonian, the unperturbed part of which generates oscillators with a cubic restoring force, is considered. It is proved that the equilibrium position is Lyapunov conditionally stable for initial values which do not belong to a certain surface of the Hamiltonian level. A reduction of the system onto this surface shows that, in the generic case, unconditional Lyapunov stability also occurs.",
author = "Bibikov, {Yu N.}",
year = "2013",
doi = "10.1016/j.jappmathmech.2013.07.006",
language = "English",
volume = "77",
pages = "167--171",
journal = "Journal of Applied Mathematics and Mechanics",
issn = "0021-8928",
publisher = "Elsevier",
number = "2",

}

RIS

TY - JOUR

T1 - The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom

AU - Bibikov, Yu N.

PY - 2013

Y1 - 2013

N2 - The stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom with a Hamiltonian, the unperturbed part of which generates oscillators with a cubic restoring force, is considered. It is proved that the equilibrium position is Lyapunov conditionally stable for initial values which do not belong to a certain surface of the Hamiltonian level. A reduction of the system onto this surface shows that, in the generic case, unconditional Lyapunov stability also occurs.

AB - The stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom with a Hamiltonian, the unperturbed part of which generates oscillators with a cubic restoring force, is considered. It is proved that the equilibrium position is Lyapunov conditionally stable for initial values which do not belong to a certain surface of the Hamiltonian level. A reduction of the system onto this surface shows that, in the generic case, unconditional Lyapunov stability also occurs.

UR - http://www.scopus.com/inward/record.url?scp=84888384175&partnerID=8YFLogxK

U2 - 10.1016/j.jappmathmech.2013.07.006

DO - 10.1016/j.jappmathmech.2013.07.006

M3 - Article

AN - SCOPUS:84888384175

VL - 77

SP - 167

EP - 171

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 2

ER -

ID: 49227140