I've read that this algorithm conserves energy if the system it's applied to conserves energy. I can't find a proof, and it's not a particularly obvious statement, so how would you prove it?
Actually, Verlet integration is approximately conserving the (total) energy, it does however preserve total angular momentum. This is the reason it is used for orbital mechanics problems. The properties of the propagation matrix of the discretized system can already give you a lot of information, especially if you do it for the hamiltonian. There is a very nice paper by Hairer, Lubich and Wanner on this topic, it is still on my 'have-to-really-read' list,
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