Motion in time of a swinging Atwood machine
Giorgio Carizi
TL;DR
This paper provides an exact analytical solution for the time-dependent motion of a swinging Atwood machine, revealing isochronous behavior related to the launch angle through advanced Hamiltonian and time transformation techniques.
Contribution
It introduces a novel exact solution for the swinging Atwood machine's motion using extended Hamiltonian and Poincare's time transformation methods.
Findings
Trajectories of teardrop-heart orbits are explicitly obtained.
The motion exhibits isochronous properties with respect to launch angle.
The approach enhances understanding of nonlinear oscillatory systems.
Abstract
An exact solution for the motion in time of the swinging Atwood machine is presented. The trajectories of the so called teardrop-heart orbits are obtained considering an extended Hamiltonian and a time transformation first introduced by Poincare. The motion is isochronous with respect to the launch angle.
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Taxonomy
TopicsSpacecraft Dynamics and Control · Experimental and Theoretical Physics Studies · Control and Dynamics of Mobile Robots