I’m trying to plot the orbits described by the solution:
x[\[Phi]_] = -(1/6)+0.5 Tanh[(\[Phi] + \[Phi]0)/2]
where the x is the radius and the [Phi]0 is the angular variable in the orbital plane. How could I plot this orbits? If it’s necessary more equations here is the complete system of ODEs:
r'[\[Lambda]_] = Sqrt[E^2 - (L^2/r^2) +(2 M L^2/r^3] \[Phi]'[\[Lambda]_] = L/(r^2) t'[\[Lambda]_] = E/(1-(2M/r))
where $ L$ is the angular momentum, $ E$ ia the total energy of the system and $ M$ is the mass of the central body.
Ps: Please, can someone edit my question I post the equations in code format, otherwise Stack wouldn’t allow me to post.
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