Limit cycles in the equation of whirling pendulum with autonomous perturbation

Hana Lichardová

Applications of Mathematics (1999)

  • Volume: 44, Issue: 4, page 271-288
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Lichardová, Hana. "Limit cycles in the equation of whirling pendulum with autonomous perturbation." Applications of Mathematics 44.4 (1999): 271-288. <http://eudml.org/doc/33034>.

@article{Lichardová1999,
abstract = {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.},
author = {Lichardová, Hana},
journal = {Applications of Mathematics},
keywords = {whirling pendulum; Hamiltonian system; autonomous perturbation; Melnikov function; limit cycle; homoclinic orbit; elliptic integral; whirling pendulum; Hamiltonian system; autonomous perturbation; Melnikov function; limit cycle; homoclinic orbit; elliptic integral},
language = {eng},
number = {4},
pages = {271-288},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Limit cycles in the equation of whirling pendulum with autonomous perturbation},
url = {http://eudml.org/doc/33034},
volume = {44},
year = {1999},
}

TY - JOUR
AU - Lichardová, Hana
TI - Limit cycles in the equation of whirling pendulum with autonomous perturbation
JO - Applications of Mathematics
PY - 1999
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 44
IS - 4
SP - 271
EP - 288
AB - 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.
LA - eng
KW - whirling pendulum; Hamiltonian system; autonomous perturbation; Melnikov function; limit cycle; homoclinic orbit; elliptic integral; whirling pendulum; Hamiltonian system; autonomous perturbation; Melnikov function; limit cycle; homoclinic orbit; elliptic integral
UR - http://eudml.org/doc/33034
ER -

References

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  7. 10.1137/0527044, Siam J. Math. Anal. 27(3) (1996), 823–834. (1996) MR1382835DOI10.1137/0527044
  8. 10.1137/0517039, SIAM J. Math. Anal. 17(3) (1986), 495–511. (1986) MR0838238DOI10.1137/0517039
  9. A Course of Modern Analysis, Cambridge at the University Press, 1927. (1927) MR1424469
  10. Global Bifurcations and Chaos: Analytical Methods, Springer Verlag, New York, Heidelberg, Berlin, 1988. (1988) Zbl0661.58001MR0956468
  11. Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer Verlag, New York, Heidelberg, Berlin, 1990. (1990) Zbl0701.58001MR1056699

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