Hamilton

J. Ocean Eng. Technol. 1996;10(3):96-104.

Hamilton

유한수심 자유표면파 문제에 적용된 해밀톤원리

김도영

홍익대학교 조선해양공학과

Keywords: Free surface wave, Variational principle, Hamilton's principle, Canonical equation, Nonlinear wave theory, Higher order wave theory, finite depth

핵심용어: 자유표면파, 변분원리, 해밀톤원리, 카노니칼방정식, 비선형파이론, 고차파이론, 유한수심

Abstract

Hamilton's principle is used to derive Euler-Lagrange equations for free surface flow problems of incompressible ideal fluid. The velocity field is chosen to satisfy the continuity equation a priori. This approach results in a hierarchial set of governing equations consist of two evolution equations with respect to two canonical variables and corresponding boundary value problems. The free surface elevation and the Lagrange's multiplier are the canonical variables in Hamilton's sense. This Lagrange's multiplier is a velocity potential defined on the free surface. Energy is conserved as a consequence of the Hamiltonian structure. These equations can be applied to waves in water of finite depth including generalization of Hamilton's equations given by Miles and Salmon.