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Currently writing and comparing two separate Mathematica scripts which can be found here and also here. The first one I've slightly modified to suit my needs and the second one is meant to reproduce the same results.

Both scripts are attempting to simulate the trajectory of a timelike geodesic using

Now, the results should be equivelent. However, my problem is as follows:

- the geodesic equations of motion.
- The Hamiltonian formalism for equations of motion.

The Hamiltonian produces a timelike geodesic that falls radially inward directly to the event horizon, where the geodesic equation approach produces a beautiful precessing orbit. Now, the approach using the geodesic equation is correct, however, can anyone see why this is different in the second link above? I have no idea why they are not producing the same results!!

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# A EoM in Schwarzschild geometry: geodesic v Hamilton formalism

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