TITLE: Swinging Atwood's Machine: experimental and theoretical studies AUTHORS: O Pujol Universit\'e de Lille, UFR de Physique fondamentale, Laboratoire d'Optique Atmosph\'erique, 59655 Villeneuve d'Ascq cedex, France E-mail:olivier.pujol@loa.univ-lille1.fr J P P\'erez Universit\'e de Toulouse, Laboratoire d'Astrophysique Toulouse-Tarbes, CNRS, 14 avenue \'Edouard Belin, 31400 Toulouse, France E-mail: perez@ast.obs-mip.fr J P Ramis Universit\'e de Toulouse, Laboratoire \'Emile Picard, 118 route de Narbonne 31062 Toulouse, France ramis.jean-pierre@wanadoo.fr C Sim\'o Universitat de Barcelona, Departament de Matem\`atica Aplicada i An\`alisi, Gran Via de les Corts Catalanes, 585, 08007 Barcelona, Spain carles@maia.ub.es S Simon University of Portsmouth, Department of Mathematics, Lion Terrace, Portsmouth, Hampshire PO1 3HF, United Kingdom Sergi.Simon@port.ac.uk J A Weil Universit\'e de Limoges, D\'epartement Math\'ematiques Informatique, XLIM - UMR CNRS n. 6172, 123 avenue Albert Thomas, 87060 Limoges cedex, France Jacques-Arthur.Weil@unilim.fr ABSTRACT: A Swinging Atwood Machine (SAM) is built and some experimental results concerning its dynamic behaviour are presented. Experiments clearly show that pulleys play a role in the motion of the pendulum, since they can rotate and have non-negligible radii and masses. Equations of motion must therefore take into account the inertial momentum of the pulleys, as well as the winding of the rope around them. Their influence is compared to previous studies. A preliminary discussion of the role of dissipation is included. The theoretical behaviour of the system with pulleys is illustrated numerically, and the relevance of different parameters is highlighted. Finally, the integrability of the dynamic system is studied, the main result being that the Machine with pulleys is non-integrable. The status of the results on integrability of the pulley-less Machine is also recalled.