The geodesic equation can be solved via some ode-solver, for example RK45. In each step I get the tangent vector as well as the new position. As the equation is only valid for arc length parametrezised curves the tangent vector norm equals to $1$. In my numerical calculations, this tangent vector norm varies but is not constantly equal to $1$.
How shall I deal with it?
To calculate the correct curve, it does not make sense to me that the norm of the tangent deviates from 1. Shall I in each step renorm the tangent to 1 and use it as input for the next step?
