| Hamilton-Jacobi theory [`ham·ǝl·tǝn jǝ`kō·bē ´thē·ǝ·rē] MATHEMATICS The study of the solutions of the Hamilton-Jacobi equation and the information they provide concerning solutions of the related systems of ordinary differential equations. MECHANICS A theory that provides a means for discussing the motion of a dynamic system in terms of a single partial differential equation of the first order, the Hamilton-Jacobi equation. |