Wednesday, February 8, 2012

Pairwise force functions

Using the abbreviated characters u = u(x,t) and u' = u(x',t) Newton's third law places the afterward brake on f:

\displaystyle f(u-u', x-x', x') = -f(u'-u, x'-x, x)

for any x,x',u,u'. This blueprint states that the force body agent that x exerts on x' equals bare the force body agent that x' exerts on x. Balance of angular drive requires that f be alongside to the agent abutting the askew position of x to the askew position of x':

\displaystyle ((x'+u')-(x+u))\times f(u'-u, x'-x, x)=0.

A pairwise force action is authentic by a blueprint of | f | against band addendum e, authentic by

\displaystyle e=|(x'+u')-(x+u)|-|x'-x|.

A schematic of a pairwise force action for the band abutting two archetypal credibility is apparent in the afterward figure:

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