| Title:
|
The period of a whirling pendulum (English) |
| Author:
|
Lichardová, Hana |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
593-606 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The period function of a planar parameter-depending Hamiltonian system is examined. It is proved that, depending on the value of the parameter, it is either monotone or has exactly one critical point. (English) |
| Keyword:
|
Hamiltonian system |
| Keyword:
|
period function |
| Keyword:
|
Picard-Fuchs equations |
| MSC:
|
34C05 |
| MSC:
|
37G15 |
| idZBL:
|
Zbl 0977.37027 |
| idMR:
|
MR1970262 |
| DOI:
|
10.21136/MB.2001.134193 |
| . |
| Date available:
|
2009-09-24T21:54:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134193 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Chicone, C.: The monotonicity of the period function for planar hamiltonian vector fields.J. Differ. Equations 69 (1987), 310–321. Zbl 0622.34033, MR 0903390, 10.1016/0022-0396(87)90122-7 |
| Reference:
|
[4] Chow, S.-N., Sanders, J. A.: On the number of critical points of the period.J. Differ. Equations 64 (1986), 51–66. MR 0849664, 10.1016/0022-0396(86)90071-9 |
| Reference:
|
[5] Chow, S.-N., Hale, J. K.: Methods of Bifurcation Theory.Springer, New York, 1996. MR 0660633 |
| Reference:
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| Reference:
|
[7] Cushman, R., Sanders, J. A: A codimension two bifurcation with a third order Picard-Fuchs equation.J. Differ. Equations 59 (1985), 243–256. MR 0804890, 10.1016/0022-0396(85)90156-1 |
| Reference:
|
[8] Guckenheimer, J., Holmes, P. J.: Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields.Springer, New York, 1983. MR 0709768 |
| Reference:
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[9] Jarník, V.: Integral Calculus II.Academia, Praha, 1976. (Czech) |
| Reference:
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[10] Kauderer, H.: Nichtlineare Mechanik.Springer, Berlin, 1958. Zbl 0080.17409, MR 0145709 |
| Reference:
|
[11] Lichardová, H.: Limit cycles in the equation of whirling pendulum with autonomous perturbation.Appl. Math. 44 (1999), 271–288. MR 1698769, 10.1023/A:1023080513150 |
| Reference:
|
[12] Qiu, S.-L., Vamanamurthy, M. K.: Sharp estimates for complete elliptic integrals.SIAM J. Math. Anal. 27 (1996), 823–834. MR 1382835, 10.1137/0527044 |
| Reference:
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[13] Sanders, J. A., Cushman, R.: Limit cycles in the Josephson equation.SIAM J. Math. Anal. 17 (1986), 495–511. MR 0838238, 10.1137/0517039 |
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| Reference:
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| . |
