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.
The role of symplectic integrators in optimal control
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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.