Symplectic Euler's modified Hamiltonian is not invariant under non-affine coordinate changes, and a new condition predicts when a cyclic-coordinate first integral is lost.
OrbitN: A Symplectic Integrator for Planetary Systems Dominated by a Central Mass—Insight into Long-term Solar System Chaos
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On the coordinate system-dependence of the accuracy of symplectic numerical methods
Symplectic Euler's modified Hamiltonian is not invariant under non-affine coordinate changes, and a new condition predicts when a cyclic-coordinate first integral is lost.