| Title:
|
Limit cycles in the equation of whirling pendulum with autonomous perturbation (English) |
| Author:
|
Lichardová, Hana |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
271-288 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the Mel’nikov method, existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters is proved. (English) |
| Keyword:
|
whirling pendulum |
| Keyword:
|
Hamiltonian system |
| Keyword:
|
autonomous perturbation |
| Keyword:
|
Melnikov function |
| Keyword:
|
limit cycle |
| Keyword:
|
homoclinic orbit |
| Keyword:
|
elliptic integral |
| MSC:
|
34C05 |
| MSC:
|
34C23 |
| MSC:
|
37G15 |
| MSC:
|
58F21 |
| MSC:
|
70K05 |
| idZBL:
|
Zbl 1060.34504 |
| idMR:
|
MR1698769 |
| DOI:
|
10.1023/A:1023080513150 |
| . |
| Date available:
|
2009-09-22T18:00:51Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134413 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] C. Chicone: On bifurcation of limit cycles from centers.Lecture Notes in Math., 1455, 1991, pp. 20–43. MR 1094376 |
| Reference:
|
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| Reference:
|
[5] Ch. Li and Z.-F. Zhang: A criterion for determining the monotonicity of the ratio of two abelian integrals.Journal of Differential Equations 124 (1996), 407–424. MR 1370149, 10.1006/jdeq.1996.0017 |
| Reference:
|
[6] A. D. Morozov: On limit cycles and chaos in equations of pendulum type.Prikladnaja matematika i mechanika 53(5) (1989), 721–730. (Russian) MR 1040438 |
| Reference:
|
[7] S.-L.Qiu and M. K. Vamanamurthy: Sharp estimates for complete elliptic integrals.Siam J. Math. Anal. 27(3) (1996), 823–834. MR 1382835, 10.1137/0527044 |
| Reference:
|
[8] J.A. Sanders and R. Cushman: Limit cycles in the Josephson equation.SIAM J. Math. Anal. 17(3) (1986), 495–511. MR 0838238, 10.1137/0517039 |
| Reference:
|
[9] E. T. Whittaker and G. N. Watson: A Course of Modern Analysis.Cambridge at the University Press, 1927. MR 1424469 |
| Reference:
|
[10] S. Wiggins: Global Bifurcations and Chaos: Analytical Methods.Springer Verlag, New York, Heidelberg, Berlin, 1988. Zbl 0661.58001, MR 0956468 |
| Reference:
|
[11] S. Wiggins: Introduction to Applied Nonlinear Dynamical Systems and Chaos.Springer Verlag, New York, Heidelberg, Berlin, 1990. Zbl 0701.58001, MR 1056699 |
| . |
