Hamiltonian Formulation for Water Wave Equation

• 作者: Shamima Sultana Zillur Rahman
• 来源期刊: 流体动力学(英文)
• 学科: 数学
• 关键词: Water Wave EQUATION LAGRANGIAN FUNCTION HAMILTONIAN FUNCTION Hamilton’s CANONICAL EQUATION of Motion
• 年，卷（期）: 2013,（2）
• 页码范围: 75-81
• 页数: 7页
• 分类号: O1

摘要

This paper concerns the development and application of the Hamiltonian function which is the sum of kinetic energy and potential energy of the system. Two dimensional water wave equations for irrotational, incompressible, inviscid fluid have been constructed in cartesian coordinates and also in cylindrical coordinates. Then Lagrangian function within a certain flow region is expanded under the assumption that the dispersion μ and the nonlinearity ε satisfied . Using Hamilton’s principle for water wave evolution Hamiltonian formulation is derived. It is obvious that the motion of the system is conservative. Then Hamilton’s canonical equation of motion is also derived.