Non-Dimensionalization Mathematica

Question

I have a set of coupled equations for the variables H, W, P, & T (below) that I need to non-dimensionalize. Is there a way of achieving this in Mathematica as doing it manually is proving difficult.

{(a 1/(1 + R T[t]) - b) H[t] - (ap + bp) P[t] - bt T[t] == H'[t],

 L P[t] - g W[t] - B W[t] H[t] == W'[t],

 B  W[t] H[t] - (up + b + bp + bt T[t]/H[t]) P[t] - 
   bp (P[t]^2)/H[t] ((k + 1)/k) + phi T[t] == P'[t],

 H[t] (theta) - (b + bp P[t]/H[t] + bt ) T[t] - 
   bt (T[t]^2)/H[t] ((k + 1)/k) - v P[t] == T'[t]}

Parameter units: a = /H/unit time; b = /H/unit time; B = /H/unit time; theta = T/H/unit time; ap = /P/unit time; bp = /P/unit time; up = /P/unit time; v = /P/unit time; L = W/P/unit time; R = /T/unit time; bt = /T/unit time; phi = /T/unit time; g = /W/unit time; k = constant.

Answer 1

This package may help you to use the Pi-theorem.

I never used it, though.