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Effect of a frictional force on the Fermi-Ulam model.

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Effect of a frictional force on the Fermi-Ulam model. / Leonel, Edson D.; McClintock, Peter V. E.
In: Journal of Physics A: Mathematical and General , Vol. 39, No. 37, 15.09.2006, p. 11399-11415.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Leonel, ED & McClintock, PVE 2006, 'Effect of a frictional force on the Fermi-Ulam model.', Journal of Physics A: Mathematical and General , vol. 39, no. 37, pp. 11399-11415. https://doi.org/10.1088/0305-4470/39/37/005

APA

Leonel, E. D., & McClintock, P. V. E. (2006). Effect of a frictional force on the Fermi-Ulam model. Journal of Physics A: Mathematical and General , 39(37), 11399-11415. https://doi.org/10.1088/0305-4470/39/37/005

Vancouver

Leonel ED, McClintock PVE. Effect of a frictional force on the Fermi-Ulam model. Journal of Physics A: Mathematical and General . 2006 Sept 15;39(37):11399-11415. doi: 10.1088/0305-4470/39/37/005

Author

Leonel, Edson D. ; McClintock, Peter V. E. / Effect of a frictional force on the Fermi-Ulam model. In: Journal of Physics A: Mathematical and General . 2006 ; Vol. 39, No. 37. pp. 11399-11415.

Bibtex

@article{df2316793eef4210a0f9bd924f76f0b3,
title = "Effect of a frictional force on the Fermi-Ulam model.",
abstract = "The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi–Ulam model as the drag force goes to zero.",
author = "Leonel, {Edson D.} and McClintock, {Peter V. E.}",
year = "2006",
month = sep,
day = "15",
doi = "10.1088/0305-4470/39/37/005",
language = "English",
volume = "39",
pages = "11399--11415",
journal = "Journal of Physics A: Mathematical and General ",
issn = "0305-4470",
publisher = "IOP Publishing Ltd",
number = "37",

}

RIS

TY - JOUR

T1 - Effect of a frictional force on the Fermi-Ulam model.

AU - Leonel, Edson D.

AU - McClintock, Peter V. E.

PY - 2006/9/15

Y1 - 2006/9/15

N2 - The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi–Ulam model as the drag force goes to zero.

AB - The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi–Ulam model as the drag force goes to zero.

U2 - 10.1088/0305-4470/39/37/005

DO - 10.1088/0305-4470/39/37/005

M3 - Journal article

VL - 39

SP - 11399

EP - 11415

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 0305-4470

IS - 37

ER -