Swinging Atwood’s Machine

Tufillaro, Nicholas B.; Abbott, Tyler A.; Griffiths, David J.

doi:10.1119/1.13791

Cited by 34 publications

(21 citation statements)

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“…pulley inertial momentum I p = 0 and pulley radius R = 0, we recover the equations obtained by [30]:…”

Section: Comparison With Previous Studiessupporting

confidence: 70%

“…An important point concerns the comparison between these trajectories and those of [30]. For the first case for instance, Tufillaro's trajectories are symmetrical with respect to the vertical direction, as opposed to the above ones (Figures 7a and 12a).…”

Section: Theoretical Trajectoriesmentioning

confidence: 99%

“…Let us determine the equations of motion for SAM by taking into account the pulleys, as opposed to what has been assumed in previous theoretical studies [19,20,27,28,29,30,31,35]. Indeed, their non-zero radii imply a likely change in position for Q, and the equally likely rotation of P and P ′ around their respective revolution axes apparently deems their inertial momentum I p a significant dynamic parameter.…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Said studies were conducted exclusively on a simplified model for SAM neglecting any influence from a massive set of pulleys. Through numerical investigations, [30] inferred the pulley-less SAM to be an extremely intricate system exhibiting significant changes in the qualitative behaviour of trajectories, depending on µ-values. Assuming µ > 1, motion is limited in space and two types of trajectories can be distinguished owing to the initial conditions: singular ones for which pendulum length is initially zero, and non-singular ones where the pendulum is initially released from rest with a non-zero length.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Swinging Atwood Machine: Experimental and numerical results, and a theoretical study

Pujol¹,

Pérez²,

Ramis³

et al. 2010

Physica D: Nonlinear Phenomena

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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.Key words: Swinging Atwood's Machine (SAM ), Chaotic system, Nonlinear dynamics, Integrability, Experimental SAM apparatus. * Corresponding author Email addresses: olivier.pujol@loa.univ-lille1.fr (O Pujol), perez@ast.obs-mip.fr (J P Pérez), ramis.jean-pierre@wanadoo.fr (J P Ramis), carles@maia.ub.es (C Simó), Sergi.Simon@port.ac.uk (S Simon), Jacques-Arthur.Weil@unilim.fr (J A Weil)

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“…pulley inertial momentum I p = 0 and pulley radius R = 0, we recover the equations obtained by [30]:…”

Section: Comparison With Previous Studiessupporting

confidence: 70%

Section: Theoretical Trajectoriesmentioning

confidence: 99%

Section: Equations Of Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Swinging Atwood Machine: Experimental and numerical results, and a theoretical study

Pujol¹,

Pérez²,

Ramis³

et al. 2010

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…It should be noted that swinging Atwood's machine has been a subject of a number of papers (see [2][3][4][5][6][7][8]) and its mechanical behaviour has been studied quite well. In particular, it has been proven that the system of differential equations describing dynamics of swinging Atwood's machine is not integrable, in general.…”

Section: Introductionmentioning

confidence: 99%

Motion of a Swinging Atwood’s Machine: Simulation and Analysis with Mathematica

Prokopenya

2017

Math.Comput.Sci.

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A generalized model of the Atwood machine when one body is constrained to move along a vertical axis while the other one can swing in a plane is considered. Combining symbolic and numerical calculations, we have obtained equations of motion of the system and analyzed their solutions. We have shown that oscillation can completely modify a motion of the system while the simple Atwood machine demonstrates only the uniformly accelerated motion of the bodies. The validity of the results obtained is demonstrated by means of the simulation of motion of swinging Atwood's machine with the computer algebra system Wolfram Mathematica.

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Stability Analysis of Periodic Motion of the Swinging Atwood Machine

Prokopenya

2022

Computer Algebra in Scientific Computing

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Swinging Atwood’s Machine

Cited by 34 publications

References 0 publications

Swinging Atwood Machine: Experimental and numerical results, and a theoretical study

Swinging Atwood Machine: Experimental and numerical results, and a theoretical study

Motion of a Swinging Atwood’s Machine: Simulation and Analysis with Mathematica

Stability Analysis of Periodic Motion of the Swinging Atwood Machine

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