The Cayley-Menger Determinant, D(N), slickly calculates the N-dimensional simplex volume of any N+1 points. One constraint in our 3D world is that D(4)=0.

Give each point a mass (Mi) and dynamic interdistances (i.e., Rij(t) are functions of "time") according to inertia and non-relativistic "Newtonian gravity". Is there a simple mathematical way to express the resulting dynamic constraints in these terms?

I'm basically wondering if these interdistances are somehow superior to normal coordinates in multi-body problems, but gravity doesn't appear to fit nicely...sorry for the vague question!