# Focal Attraction with Rotation

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This Demonstration uses *Mathematica*'s NDSolve to plot trajectories of the Markus–Wilson model of focal attraction on a rotating medium. This dynamical system is parameterized by four positive parameters, , , , and , which correspond to physical parameters of the model: describes the rotational speed, quantifies the radial drift in the model (the default is zero, i.e., no drift), is the magnitude of the focal attraction whose source is at in Euclidean coordinates, where is the size of the rotating disk. To see how the trajectory develops through time (and hopefully its asymptotic behavior), autorun through the parameter. For large this may result in slow rendering of the smoothed curve.

Contributed by: Jorge Sotomayor and Steven Broad (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

For a more detailed discussion of this model please see http://arxiv.org/abs/0801.4500. This paper by Jorge Sotomayor describes this model and some possible improvements that might allow one to better understand the parameter space. The idea for this model was taken from H. K. Wilson, *Ordinary Differential Equations*, Reading, MA.: Addison–Wesley, 1971. One may also refer to Jorge Sotomayor, *Liçoes de Equaçoes Diferenciais Ordinárias*, Rio de Janeiro: IMPA, 1979 (in Portuguese).

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