TY - JOUR
T1 - Swinging Atwood Machine: experimental and numerical results and a theoretical study
AU - Pujol, O.
AU - Perez, J.
AU - Ramis, J.
AU - Simo, C.
AU - Simon, Sergi
AU - Weil, J.
PY - 2010
Y1 - 2010
N2 - 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 moment of inertia 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.
AB - 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 moment of inertia 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.
U2 - 10.1016/j.physd.2010.02.017
DO - 10.1016/j.physd.2010.02.017
M3 - Article
SN - 0167-2789
VL - 239
SP - 1067
EP - 1081
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 12
ER -