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

In: Journal of Applied Mathematics and Mechanics, Vol. 77, No. 2, 2013, p. 167-171.

Research output: Contribution to journal › Article › peer-review

Harvard

Bibikov, YN 2013, 'The stability of the equilibrium position of Hamiltonian systems with two degrees of freedom', Journal of Applied Mathematics and Mechanics, vol. 77, no. 2, pp. 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. In: Journal of Applied Mathematics and Mechanics. 2013 ; Vol. 77, No. 2. pp. 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