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## Main Question or Discussion Point

hi there,

I'm trying to plot r against [tex]\phi[/tex] by solving the following ODEs using runge-kutta. The problem i'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :).

E and L and M are constants.

r>0.

[tex]

V^2(r) = \left(1 - \frac{2M}{r} \right)\frac{L^2}{r^2}

[/tex]

[tex]

\frac{d \phi}{d \lambda} &= \frac{L}{r^2}

[/tex]

[tex]

\frac{dr}{d\lambda} &= \pm\sqrt{E^2 - V^2(r)}

[/tex]

Thanks

I'm trying to plot r against [tex]\phi[/tex] by solving the following ODEs using runge-kutta. The problem i'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :).

E and L and M are constants.

r>0.

[tex]

V^2(r) = \left(1 - \frac{2M}{r} \right)\frac{L^2}{r^2}

[/tex]

[tex]

\frac{d \phi}{d \lambda} &= \frac{L}{r^2}

[/tex]

[tex]

\frac{dr}{d\lambda} &= \pm\sqrt{E^2 - V^2(r)}

[/tex]

Thanks

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