Comments on: Spring Physics

By: Peter

Peter — Sun, 20 Jun 2010 18:29:40 +0000

You might want to explore my App – 4 springs and one mass -
http://www.itunes.com/app/springsnthingslite

It uses the Euler-Cromer algorithm which is much better than just Euler because it conserves energy when there is no damping. Cromer tells us to take a half step in approximating the velocity. The full version of Springs’nThings lets you adjust spring damping, pendulum damping, mass, etc.

Hope your readers (those with an iPhone/iPad/ITouch) enjoy it.

Peter

By: Glenn Fiedler

Glenn Fiedler — Mon, 29 Mar 2010 15:32:22 +0000

that’s very interesting david, thanks for the info!

By: David

David — Sun, 28 Mar 2010 14:58:08 +0000

I found that advancing all bodies together in each RK4 substep tends to increase the total energy of the system (i.e. explode) more quickly than advancing each body through all RK4 substeps separately. However, advancing each body through all RK4 substeps separately seems to lead to higher systematic errors. For example, the center of mass of a two-mass oscillator tends to float in the direction of the mass which is integrated last.

Based on what I found, I personally prefer advancing each body through all substeps separately: it’s easier to code and seems to be less prone to explosions in complex systems.

By: Glenn Fiedler

Glenn Fiedler — Wed, 17 Feb 2010 05:45:45 +0000

Fixed now.

By: Glenn Fiedler

Glenn Fiedler — Tue, 16 Feb 2010 17:17:14 +0000

You are correct, the way I’ve described it in the article is only correct if the rest length is zero. I’ll fix it up.

By: Jack

Jack — Tue, 16 Feb 2010 10:40:06 +0000

Hi!
I want to point out that, actually, your description of equation on springs and dampers is completely wrong. F= -kx .where x is not LENGTH of the string but actually the difference(with sign) between length of relaxed spring and the spring stretched/squeezed(x = deformation). So basically if spring is relaxed the force is F= -k *0 = 0 ; and when lets say its stretched 10 centimetres the F= -k*0,1= -0,1k.
so for k =1;
normal spring x=0;
stretched spring x= 0,1m : F=-0,1 force is negative to the force you use to stretch.
squeezed spring x=-0,1m : F=0,1 force is again negative to the force you stretch with, but actually you squeeze, so it want to be relaxed again.

BTW. Really great articles!

By: Glenn Fiedler

Glenn Fiedler — Thu, 10 Sep 2009 00:15:51 +0000

in order to get the full benefits of RK4 you must advance each group of interacting bodies together in each RK4 substep — if the cost of this is too great, you could consider using a velocity verlet integrator instead

http://en.wikipedia.org/wiki/Verlet_integration

cheers

By: Chris R.

Chris R. — Wed, 09 Sep 2009 22:52:47 +0000

When dealing with multiple bodies attached to each other would you argue for or against moving neighboring nodes for calculating each RK4 step?

By: Ric Wright

Ric Wright — Wed, 22 Jul 2009 19:23:16 +0000

Ah, I hadn’t actually read that article yet as my interest in networking is limited. I’ll check it out now… Thanks again. And to second (or third) the others on these threads, I would be interested in the article on collisions.

And BTW, I did donate, though not enough for two weeks of your spare time!

By: Glenn Fiedler

Glenn Fiedler — Wed, 22 Jul 2009 16:37:25 +0000

hey ric, take a look at the example for the networking article it contains spring based collisions using the RK4, cheers