| Numéro |
J. Phys. France
Volume 51, Numéro 16, août 1990
|
|
|---|---|---|
| Page(s) | 1693 - 1702 | |
| DOI | https://doi.org/10.1051/jphys:0199000510160169300 | |
J. Phys. France 51, 1693-1702 (1990)
DOI: 10.1051/jphys:0199000510160169300
1 Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Spain
2 Departamento de Fisica, Universidade de Lisboa, Portugal
3 Department of Physics, Bryn Mawr College, U.S.A.
4505 - General theory of classical mechanics of discrete systems.
Key words
integration -- pendulums
DOI: 10.1051/jphys:0199000510160169300
Swinging Atwood's Machine : integrability and dynamics
J. Casasayas1, A. Nunes2 et N. Tufillaro31 Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Spain
2 Departamento de Fisica, Universidade de Lisboa, Portugal
3 Department of Physics, Bryn Mawr College, U.S.A.
Abstract
We consider the Swinging Atwood's Machine model (SAM) and show that it is non-integrable whenever the mass ratio μ is greather than 3. This solves negatively the conjecture, based in numerical experiments, that the SAM is integrable for μ = 4 n 2 - 1, n ∈ N. We study the transversal heteroclinic orbits of the system and explain why does the system « look » integrable for these values of μ.
4505 - General theory of classical mechanics of discrete systems.
Key words
integration -- pendulums