1
$\begingroup$

I am trying to simulate the movement of a particle in a vortex in a rectangular box, I am currently using an ellipse but that causes the particle to collide with the walls more that I want.

The equation doesn't have to be exact, I am thinking for instance in to augment or reduce the mayor and minor diameter of my ellipse accordingly to, let's say the angle t in relation to angle a

I just wanted to know whether there is some equation that descrives that trajectory

Also, I want to be able to calculate the tangent vector

The following image shows what I've mentioned

http://s14.postimage.org/8cmzwwx8x/Untitled_1.png

Any help is appreciated

  • 0
    I guess is a vorticity uniformly distributed, think of a outboard motor in the x axis near one wall pointing up or down side the y axis, in that case the tangent vector magnitud could be proportional to the angle t2012-10-16

1 Answers 1

0

How about a superellipse (with $n = 4$ or $n = 6$, say): http://en.wikipedia.org/wiki/Superellipse

The article gives the parametric equations, so you can calculate derivatives (tangents).

If you're willing to use a piecewise formula, then 4 rational quadratics (i.e. conics) would work. See http://en.wikipedia.org/wiki/Bezier_curve.

  • 0
    I've tried a couple of functions on my own too, and found a very nice hyperbolic curve that appears a super-ellipse when drawn from 0 to 1, It's [ A*y - 1] * [ A*x - 1] = 1 - A; see http://s14.postimage.org/q8gvm1501/Foo_Plot_Online_graphing_calculator_and_functio.png; but even better, it looks very cheap computationaly speaking2012-10-17