AN EXTENSION OF THE HAMILTON-JACOBI METHOD

A method of solving the canonical Hamilton equations, based on a searc h for invariant manifolds, which are uniquely projected onto position space, is proposed. These manifolds are specified by covector fields, which satisfy a system of first-order partial differential equations, similar in their properties to Lamb's equations in the dynamics of an ideal fluid. If the complete integral of Lamb's equations is known, th en, with certain additional assumptions, one can integrate the initial Hamilton equations explicitly. This method reduces to the well-known Hamilton-Jacobi method for gradient fields. Some new conditions for Ha milton's equations to be accurately integrable are indicated. The gene ral results are applied to the problem of the motion of a variable bod y. (C) 1997 Elsevier Science Ltd.