The MathResource
center of mass,
n. (Continuum mechanics) 1. the weighted mean position of a finite discrete set of particles with position vectors x1,..., xn and masses m1,..., mn; its position vector is

2.. (Mechanics) (for a continuous body) the position vector given by the corresponding ratio of integrals over the volume of the configuration of the body at time t, that is,

where the density is ρ at the point with position vector x.