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From: Steven Winfield <saw44.cam.ac.uk>

Date: Thu, 15 Feb 2007 13:28:00 +0000

Hello David,

Have you tried just considering a water molecule moving in the x-y

plane? That gives you 3 force/velocity/position components you know must

always be zero... hence if you get non-zero answers for these at any

point you know there's a problem with your maths somewhere.

Steve

David Cerutti wrote:

*> Hello again,
*

*>
*

*> I've been making some headway on this constraint virial problem, and
*

*> I now know that my error involves the computation of constraint forces
*

*> for SETTLE'd water molecules.
*

*>
*

*> Does anyone know where I can find formula that tell you the forces to
*

*> apply along each of the three constrained bonds to reproduce the
*

*> accelerations that the SETTLE routine applies to the water? The problem
*

*> can be phrased fairly simply: SETTLE is considered to have applied
*

*> forces along each of the constrained bonds to return the molecule to its
*

*> original shape after a Verlet-integration (half) step deformed the water
*

*> molecule slightly. But, at the end of the SETTLE calculation, all we
*

*> have are the new velocities, from which we derive the net accelerations
*

*> and thus the net forces on each atom. Ww must account for these force
*

*> vectors with a unique set of forces acting along each of the bonds.
*

*> Three constrained bonds, three atoms and one net force on each atom
*

*> resulting from the SETTLE calculation.
*

*>
*

*> But, when I try to write down these equations and then solve for the
*

*> magnitude of the force along each bond, I run into all sorts of trouble
*

*> and I can't figure out why. It would seem that the system is
*

*> over-determined; I can write nine different equations relating each of
*

*> the three components of the three net atomic forces computed by SETTLE
*

*> to two other terms involving the forces applied along each of the bonds
*

*> ending at each of the three atoms. I can pick three of the equations
*

*> and solve them for the magnitude of the force along each bond, but for
*

*> some resaon I get different results depending on which three equations I
*

*> pick--they don't even seem to be self-consist when I look closely at the
*

*> equations.
*

*>
*

*> But, at the same time, it seems that there are three unknowns (the
*

*> magnitudes of the forces along each bond) and three knowns (the net
*

*> force on each atom applied by SETTLE) so there should be a fairly
*

*> concise solution to these equations...
*

*>
*

*> Thanks!
*

*>
*

*> Dave
*

*> -----------------------------------------------------------------------
*

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*

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Received on Sun Feb 18 2007 - 06:07:18 PST

Date: Thu, 15 Feb 2007 13:28:00 +0000

Hello David,

Have you tried just considering a water molecule moving in the x-y

plane? That gives you 3 force/velocity/position components you know must

always be zero... hence if you get non-zero answers for these at any

point you know there's a problem with your maths somewhere.

Steve

David Cerutti wrote:

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Received on Sun Feb 18 2007 - 06:07:18 PST

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