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6$\begingroup$ Thanks for your detailed response! I fixed my simulation by using the semi-implicit Euler method mentioned by Rahul. I had one more question about this method and my simulation in the comments of my post, but here it is again: Will this still work and conserve translational kinetic AND rotational kinetic energy in weird and complex force fields? I am still solving a first order differential equation for both of these, so the semi-implicit Euler method should converge on the actual solution always? Is this true? $\endgroup$– akarshkumar0101Commented Dec 31, 2019 at 19:57
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8$\begingroup$ Many quantities are conserved. In fact, Theorem 6.7 yields the conservation of quadratic first integrals $p^T A q$, such as angular momentum, by symplectic partitioned Runge–Kutta methods - a property we already know from Theorem IV.2.4. For Hamiltonian systems with an associated Lagrangian.You can easily see from this tutorial example that symplectic integrators, while they don't exactly conserve energy, do exactly conserve angular momentum. $\endgroup$– Chris RackauckasCommented Dec 31, 2019 at 20:16
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