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On stability in Hamiltonian systems with two degrees of freedom. / Bibikov, Y.N.

In: Mathematical Notes, No. 1-2, 2014, p. 174-179.

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Harvard

Bibikov, YN 2014, 'On stability in Hamiltonian systems with two degrees of freedom', Mathematical Notes, no. 1-2, pp. 174-179. https://doi.org/10.1134/S0001434614010180

APA

Bibikov, Y. N. (2014). On stability in Hamiltonian systems with two degrees of freedom. Mathematical Notes, (1-2), 174-179. https://doi.org/10.1134/S0001434614010180

Vancouver

Bibikov YN. On stability in Hamiltonian systems with two degrees of freedom. Mathematical Notes. 2014;(1-2):174-179. https://doi.org/10.1134/S0001434614010180

Author

Bibikov, Y.N. / On stability in Hamiltonian systems with two degrees of freedom. In: Mathematical Notes. 2014 ; No. 1-2. pp. 174-179.

BibTeX

@article{5a21ad9c53874eb2a7f743583891e820,
title = "On stability in Hamiltonian systems with two degrees of freedom",
abstract = "We consider the stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom whose unperturbed part describes oscillators with restoring force of odd order greater than 1. It is proved that if the exponents of the restoring force of the oscillators are not equal, then the equilibrium position is Lyapunov stable. If the exponents are equal, then the equilibrium position is conditionally stable for trajectories not belonging to some level surface of the Hamiltonian. The reduction of the system to this surface shows that the equilibrium position is stable in the case of general position. {\textcopyright} 2014 Pleiades Publishing, Ltd.",
author = "Y.N. Bibikov",
year = "2014",
doi = "10.1134/S0001434614010180",
language = "English",
pages = "174--179",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "1-2",

}

RIS

TY - JOUR

T1 - On stability in Hamiltonian systems with two degrees of freedom

AU - Bibikov, Y.N.

PY - 2014

Y1 - 2014

N2 - We consider the stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom whose unperturbed part describes oscillators with restoring force of odd order greater than 1. It is proved that if the exponents of the restoring force of the oscillators are not equal, then the equilibrium position is Lyapunov stable. If the exponents are equal, then the equilibrium position is conditionally stable for trajectories not belonging to some level surface of the Hamiltonian. The reduction of the system to this surface shows that the equilibrium position is stable in the case of general position. © 2014 Pleiades Publishing, Ltd.

AB - We consider the stability of the equilibrium position at the origin of coordinates of a Hamiltonian system with two degrees of freedom whose unperturbed part describes oscillators with restoring force of odd order greater than 1. It is proved that if the exponents of the restoring force of the oscillators are not equal, then the equilibrium position is Lyapunov stable. If the exponents are equal, then the equilibrium position is conditionally stable for trajectories not belonging to some level surface of the Hamiltonian. The reduction of the system to this surface shows that the equilibrium position is stable in the case of general position. © 2014 Pleiades Publishing, Ltd.

U2 - 10.1134/S0001434614010180

DO - 10.1134/S0001434614010180

M3 - Article

SP - 174

EP - 179

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -

ID: 7048385