= Symplectic cotangent lift with a closed momentum shift
{title2=$x=\chi(x'),\quad y=\eta\circ\chi+D\chi^{-T}y'$}
If $x=\chi(x')$ is an angular <diffeomorphism> and $\eta\cdot dx$ is a <closed differential one-form>, the map $y=\eta(\chi(x'))+D\chi(x')^{-T}y'$ is a <symplectomorphism>. It combines a <cotangent lift of a diffeomorphism> with translation by a <closed differential one-form>. In particular $\eta=du+a$ is allowed on a <torus> even when the constant one-form $a\cdot dx$ is not exact.
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