The sum of all reciprocal forces in a system of particles is always zero

up:: Newton’s Third Law

Given a system of particles , with reciprocal forces , we have that these forces can be seen as an antisymmetrical matrix

The sum of these reciprocal forces is the sum of all elements of ,

which has to be .

Corollaries

• Linear Momentum Conservation Theorem, which states that the Center of Mass behaves like a particle under the influence of (the sum of) all external forces