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L = \int_{\rho_0}^{\rho} \frac{1/c- j_m^2 / \rho}{G \, \rho^2  - F} \, d \rho
=\int_{\rho_0}^{\rho} \frac{\rho \, dp}{G \, \rho^2 - F} -\frac{j_m^2}{2} \, \ln \frac{F/\rho^2 - G}{ F/\rho_0^2-G}

F(p, l)= \int_{p_0}^p \frac{dp}{\rho} -g \, \Delta z(l)
+ 0.5 \cdot j_m^2 \cdot 
\left(  \frac{1}{\rho^2} - \frac{1}{\rho_0^2}   \right)  
+
\frac{16 \, l \, j_m}{d^2} \cdot
\left(  \frac{\mu \, \Phi}{\rho^2} + \frac{\mu_0 \, \Phi_0}{\rho_0^2}  \right)  
= 0...