Chambers wrote:
> Here's a test app for Windows:
> 
> http://www.pacificwebguy.com/downloads/TestingRK4.zip
> (Note that, although the app itself is named "Threaded_Physics.exe", I 
> haven't gotten around to implementing the "threaded" part yet.  Right 
> now, I'm just trying to make it work *correctly*).
> 
> Click anywhere on the screen to shoot particles in that direction.
> Press F1 to switch between Newtonian integration and Rk4 integration.
> 
> The main thing to notice, other than the fact that RK4 is *much* slower 
> than Newtonian, is that using RK4 seems to amplify the forces somehow. 
> The result is that everything seems rather... well, crazy.  In contrast, 
> I've reached a point where the Newtonian doesn't look quite so bad 
> (although I'd still like to work on the speed factor a bit).
> 
> Here's the inside of the RK4 integrator, as I implemented it:
> 
> {
>  collide(particles_now, forces_now, gravity);
>  step(particles_now, particles_stepped, forces_now, dt/2);
>  collide(particles_stepped, forces_A, gravity);
>  step(particles_now, particles_stepped, forces_A, dt/2);
>  collide(particles_stepped, forces_B, gravity);
>  step(particles_now, particles_stepped, forces_B, dt);
>  collide(particles_stepped, forces_C, gravity);
>  for (int i=0; i<size; i++) {
>   forces_final[i] =
>    (forces_now[i]+2*forces_A[i]+2*forces_B[i]+forces_C[i])/6.0f;
>  }
>  step(particles_now, particles_now, forces_final, dt);
> }
> 
> And stubbed headers for the functions:
> 
> collide(data, result, gravity)
> This calculates the collisions between particles, and the resultant 
> forces (gravity is used as the initial, or base, force to start with)
> 
> step(data, result, forces, dt)
> Applies forces to data with a timestep of dt
> 
> PS I just got a collection of all of Chopin's piano music (something 
> like 15 CDs), and it's great "productivity" music (ie, have on in the 
> background while I'm working on something else) :)

The last time I did a physics simulator (springs and weights), I found 
that calculating the change in acceleration, and figuring that into the 
new location and velocity data, greatly reduced the error that accumulates.

Regards,
John

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