The Velocity Verlet Algorithm is confirmed to conserve energy in systems that inherently conserve energy, particularly in orbital mechanics applications. While it does not provide a straightforward proof, it is known to approximately conserve total energy and preserve total angular momentum. The properties of the propagation matrix of the discretized system, especially when analyzed through the Hamiltonian, offer significant insights into energy conservation. A key reference for further understanding is the paper by Hairer, Lubich, and Wanner, specifically chapter 5, which addresses energy conservation in detail.
PREREQUISITESResearchers in computational physics, students studying classical mechanics, and professionals working on simulations in orbital mechanics or molecular dynamics will benefit from this discussion.