Mean velocity of a kinetic distribution ($u=\frac{\int vf(x,v)dxdv}{\int f(x,v)dxdv}$)

The mass-normalized first velocity moment of a distribution on phase space. For a velocity-only distribution, omit the position integral. Nonzero finite mass and a finite first moment are required. For a probability distribution this is its expected value; its unnormalized counterpart is the momentum.