The Lagrange–Charpit Theory of the Hamilton–Jacobi Problem

Abstract The Lagrange–Charpit theory is a geometric method of determining complete integral by means constant the motion vector field defined on phase space associated to nonlinear PDE first order. In this article, we establish symplectic structure cotangent bundle $$T^{*}Q$$ T ∗ Q configuration manifold Q . particular, use it calculate explicitly isotropic submanifolds with Hamilton–Jacobi equation.