= Hyperregular Lagrangian
{title2=$\mathbb FL:TQ\overset{\sim}{\longrightarrow}T^*Q$}
A <Lagrangian> is hyperregular when its fiber derivative, sending a velocity to its conjugate momentum, is a global <diffeomorphism> from the <tangent bundle> to the <cotangent bundle>. This gives a globally defined <Legendre transform in mechanics> and a global equivalence between the <Euler-Lagrange equations> and <Hamilton's equations>. With time dependence this requirement is imposed at each time, with a smooth inverse depending on time.
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