Abstract
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.
Highlights
Dynamics research on Hamilton systems is an important subject in mechanics for a long time
The principles of Hamilton mechanics settled a series of problems effectively that could not be solved by other methods, which showed theoretically the importance of Hamilton mechanics
There are mainly two variational formulations for irrotational surface waves that are commonly used in Luke [2] and Zakharov [3]
Summary
Dynamics research on Hamilton systems is an important subject in mechanics for a long time. The water wave problem is known to have the multi-simplistic structure These Hamilton’s principles have been used to build an analytical approximation. We emphasize that our primary purpose here is to provide a generalized framework for deriving model equations for water waves This methodology is explained on various examples; some of them are new to our knowledge. This Hamilton’s principle for incompressible and inviscid fluid is used to derive approximate wave models. Zakharov [3] showed that the water elevation and the potential at the free surface are canonical variables when formulating the water-waves problem in Hamiltonian formalism. Hamiltonian formulation within a certain flow region for shallow water wave has been constructed and Hamilton’s canonical equation of motion is derived
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