= Regular Lagrangian
{title2=$\det(L_{v^iv^j})\ne0$}
A <Lagrangian> is regular when its velocity <Hessian matrix> is invertible. The <inverse function theorem> then makes the fiber derivative $p_i=L_{v^i}$ locally invertible, allowing a local <Legendre transform in mechanics> to a <Hamiltonian>. If that fiber derivative is globally invertible, the <Lagrangian> is called a <hyperregular Lagrangian>. Regularity alone does not assert global invertibility, and singular <Lagrangians> may give constrained rather than ordinary unconstrained <Hamilton's equations>.
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