Non-Dimensionalization Mathematica
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:开发者_StackOverflow社区 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.
This package may help you to use the Pi-theorem.
I never used it, though.
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