\(H = \sum p_i\dot{q_i} - L\), where \(p_i\) is a generalized momentum, \(\dot{q_i}\) is a generalized velocity, and \(L\) is the Lagrange function.
n3:plainTextDescription
The Hamilton–Jacobi equation (HJE) is a necessary condition describing extremal geometry in generalizations of problems from the calculus of variations.