Abstract
The Melnikov function for the prediction of Smale horseshoe chaos is applied to a driven damped pendulum with variable length. Depending on the parameters, it is shown that this dynamical system undertakes heteroclinic bifurcations which are the source of the unstable chaotic motion. The analytical results are illustrated by new numerical simulations. Furthermore, using the averaging theorem, the stability of the subharmonics is studied.
Citation Formats
Bartuccelli, M, Christiansen, P L, Muto, V, Soerensen, M P, and Pedersen, N F.
Chaotic behaviour of a pendulum with variable length.
Italy: N. p.,
1987.
Web.
Bartuccelli, M, Christiansen, P L, Muto, V, Soerensen, M P, & Pedersen, N F.
Chaotic behaviour of a pendulum with variable length.
Italy.
Bartuccelli, M, Christiansen, P L, Muto, V, Soerensen, M P, and Pedersen, N F.
1987.
"Chaotic behaviour of a pendulum with variable length."
Italy.
@misc{etde_5120239,
title = {Chaotic behaviour of a pendulum with variable length}
author = {Bartuccelli, M, Christiansen, P L, Muto, V, Soerensen, M P, and Pedersen, N F}
abstractNote = {The Melnikov function for the prediction of Smale horseshoe chaos is applied to a driven damped pendulum with variable length. Depending on the parameters, it is shown that this dynamical system undertakes heteroclinic bifurcations which are the source of the unstable chaotic motion. The analytical results are illustrated by new numerical simulations. Furthermore, using the averaging theorem, the stability of the subharmonics is studied.}
journal = []
volume = {100:2}
journal type = {AC}
place = {Italy}
year = {1987}
month = {Aug}
}
title = {Chaotic behaviour of a pendulum with variable length}
author = {Bartuccelli, M, Christiansen, P L, Muto, V, Soerensen, M P, and Pedersen, N F}
abstractNote = {The Melnikov function for the prediction of Smale horseshoe chaos is applied to a driven damped pendulum with variable length. Depending on the parameters, it is shown that this dynamical system undertakes heteroclinic bifurcations which are the source of the unstable chaotic motion. The analytical results are illustrated by new numerical simulations. Furthermore, using the averaging theorem, the stability of the subharmonics is studied.}
journal = []
volume = {100:2}
journal type = {AC}
place = {Italy}
year = {1987}
month = {Aug}
}