J. Phys. France
Volume 51, Numéro 16, août 1990
Page(s) 1693 - 1702
J. Phys. France 51, 1693-1702 (1990)
DOI: 10.1051/jphys:0199000510160169300

Swinging Atwood's Machine : integrability and dynamics

J. Casasayas1, A. Nunes2 et N. Tufillaro3

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.

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