 Mechanical similarity

In classical mechanics, a branch overlapping in physics and applied mathematics, mechanical similarity occurs when the potential energy is a homogeneous function of the positions of the particles, with the result that the trajectories of the particles in the system are geometrically similar paths, differing in size but retaining shape.Consider a system of any number of particles and assume that the interaction energy between any pair of particles has the form 

where "r" is the distance between the two particles.