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n = \frac{f \, L^*}{2 \, d}

L^* = \frac{1}{2 \, G \, c^* \, \rho^*}

\rho_0/\rho = \frac{1+c^* p_0}{1+c^* p}

q_0^2 = \frac{A^2}{c^* \rho^*} \cdot \frac{1 - (\rho/\rho_0)^2 \cdot \exp \left(  -L/ L^* \right)}{2 \ln (\rho_0/\rho) + fL/d \cdot (1- \exp \left(  - L/ L^* \right))/(L/L^*)}

\dot m^2 = \frac{A^2}{c^* \rho^*} \cdot \frac{\rho_0^2 - \rho^2 \cdot \exp \left(  -L/ L^* \right)}{2 \ln (\rho_0/\rho) + fL/d \cdot (1- \exp \left(  - L/ L^* \right))/(L/L^*)}

\rho = \rho_0 \, \exp (c^* \rho^*2 \, G \, LL/L^*) \cdot \sqrt{ 1 - \frac{f}{2d} \cdot \frac{j_m^2}{G \, \rho_0^2} \cdot ( 1 - \exp(-2 \, c^* \rho^* \, G \, L)L/L^*)}

p(L) = \frac{1}{c^*} \cdot \left[ 
-1 + (1+c^* p_0) \cdot \exp (c^* \rho^*2 \, G \, LL/L^*) \cdot \sqrt{  1 - \frac{f}{2d}  \cdot \frac{j_m^2}{G \rho_0^2} \cdot \bigleft(1 - \exp (-2 \, c^* \rho^* \, G \, LL/L^*) \bigright) }
\right]

\rho = \rho_0 \, \exp (L/L^*)

p(L) = \frac{-1 + (1+c^* \, p_0) \cdot \exp(L/L^*)}{c^*}