146 research outputs found
Swinging Atwood's Machine: Experimental and Theoretical Studies
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.Comment: 37 page
Templates and Framed Braids
We show how a template for a dynamical system can be uniquely specified by a framed braid. This leads to a homological classification of strange attractors in terms of an associated linking matrix
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