An extension of the Hamilton-Jacobi method

✍ Scribed by V.V. Kozlov

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 659 KB
• Volume: 60
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(96)00113-x

✦ Synopsis

A method of solving the canonical Hamilton equations, based on a search 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 lcaown, then, with certain additional assumptions, one can integrate the initial Hamilton equations explicitly. This method reduces to lhe well-known Hamilton-Jacobi method for gradient fields. Some new conditions for Hamilton's equations to be accurately integrable are indicated. The general results are applied to the problem of the motion of a variable body.