N-body Potential Reduction: Can It Be Done?

Thread starter Päällikkö
Start date Jan 29, 2010
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Potentials

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The discussion explores the possibility of reducing n-body potentials to functions of the distances between particles, similar to the two-body case. It questions whether this reduction can be achieved without additional constraints, assuming point particles without internal structure. The focus is on representations of angular and dihedral potentials. The initial assessment suggests that the reduction may be feasible for three point particles due to triangle congruence principles. Further insights and ideas on this topic are sought from participants.

Jan 29, 2010

Päällikkö

Homework Helper

I suppose I could've equally well posted this to the math forum, but here goes...

One often sees the two-body potential f(r₁, r₂) being reduced to to f(r₁₂). Can this be done in a more general case (can n-body potentials be reduced to just the distances between all the particles, e.g. f(r₁, r₂) -> f(r₁₂, r₁₃, r₂₃))? I assume that the point particles don't have any internal structure. Do I need to add further constraints? I'm mainly aiming for representations of angular and dihedral (torsional) potentials.

From the looks of it, I'd guess it works at least with 3 point particles, due to the SSS triangle congruence.

Any ideas?

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