Our experiment is described by 3 equations: Newton's law of motion (F=ma), Gauss's law (divE=ρ) and continuity equation (D/Dt=0). These are in general 3 first order, coupled differential equations with 3 unknowns. When I tried to solve them analytically and get a single equation for one unknown function only, I quickly realized that it's pointless: I will get a 3rd order nonlinear differential equation, with derivatives with respect to both my variables, plus terms of all the possible combinations of cross derivatives, plus nonlinear terms with derivatives squared and cubed. I didn't fully derive this equation because even if I do, how the fuck am I going to ever solve it?
Hence the only solution I see is to go back to the original, simpler 3 equations and try to solve them numerically. Can Matlab do it?
