Hey! I can see this forum is stagnating... so let's revive it!

Here is my problem:

When I move a body (particle, object, whatever), I always add the acceleration to the velocity and the velocity to the position of the object. That's basic physics, ryt?

However, when Im tryin to make it approach an axis, it goes into simple harmonic motion. I know that's due to my environment's lack of friction.

So I went through my physics books and found a lot of formulae linking displacement and time with damping, but my problem is that I don't move my particles depending on time, but depending on their distance to where I want to move them to.

Im sure most of you have come across this, so I was wondering if you could help me out.

What Im looking for is 2 things: a way to create damped harmonic motion, and a way to create a hyperbola-type motion, i.e. smoothly approching an asymptote without crossing it.

Thanks for your help
Cheers