[ODE] ODE with non-penetration constraint
Nguyen Binh
ngbinh at gmail.com
Thu Jul 12 12:58:56 MST 2007
But ODE still solve for constraint forces. That makes me refer to ODE as
acceleration-force model.
The equations you showed are basically discretized version of Newton-Euler
equation. And yes, ODE use velocity as variables there.
On 7/12/07, Dirk Gregorius <dirk at dirkgregorius.de> wrote:
>
> Nguyen,
>
> I would argue that the ODE solves on the velocity level. Basically you
> have an DAE (for simplicity for holonom constraints):
>
> dv/dt = W * ( F_ext + JT * lambda )
> dx/dt = v
>
> C(p,q) = 0
>
> We use the differential quotient for the accelerations:
>
> dv/dt ~= ( v(t+dt) - v(t) ) / dt -> v(t+dt) = v(t) + W * ( F_ext + JT *
> lambda ) * dt
>
> We can find the velocity constraints through differentiation of the
> position constraints
>
> dC/dt = dC/dx * dx/dt = J * v(t) = 0
>
> Since we use the velocities of the end of the timestep (Symplectic Euler)
> we can require J * v(t+dt) = 0
>
> If you combine these equations you end up with the well know LS (or MLCP
> in the presence of non-holonom constraints)
>
> J*W*JT*lambda = -( v(t)/dt + W * f_ext )
>
> You could multiply the whole equation by dt > 0 and get
>
> J*W*JT*(lambda*dt) = -( v(t) + W * f_ext * dt )
>
> You clearly see the forces and impulses are linear related in this model.
> Also I argue that in every discrete model a constraint can't break. Of
> course a constraint force could become zero (through clamping), but the ODE
> can handle this as well.
>
>
>
> So regarding the original question. Because of the discrete collision
> model you can end up in penetration. This has nothing todo with hard or soft
> constraints. The ERP parameter basically handles how much of the error is
> corrected each timestep. Also note that ODE has some value that allows for
> some penetration before the error correction jumps in. This is in order to
> deal with jitter and to improve coherence. So the 0.005 you see might be
> the default value for the allowed penetration.
>
> HTH,
> -Dirk
>
>
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>
--
--------------------------------------------------
Binh Nguyen
Computer Science Department
Rensselaer Polytechnic Institute
Troy, NY, 12180
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