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
Any help is appreciated