The Legendre transform L(q, q̇) ↦ H(q, p) = sup_q̇ (p·q̇ − L) is a fibre-wise convex duality which, under non-degeneracy of the Hessian ∂²L/∂q̇² (hyper-regular Lagrangian), promotes the Euler–Lagrange equations on TQ to Hamilton's…
The Legendre transform L(q, q̇) ↦ H(q, p) = sup_q̇ (p·q̇ − L) is a fibre-wise convex duality which, under non-degeneracy of the Hessian ∂²L/∂q̇² (hyper-regular Lagrangian), promotes the Euler–Lagrange equations on TQ to Hamilton's…