Kirchhoff's equations of motion via a constrained Zakharov system

Banavara N.  Shashikanth

doi:10.3934/jgm.2016016

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2016, Volume 8, Issue 4: 461-485. Doi: 10.3934/jgm.2016016

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Kirchhoff's equations of motion via a constrained Zakharov system

Banavara N. Shashikanth^1,

1.
Mechanical and Aerospace Engineering Department, MSC 3450, PO Box 30001, New Mexico State University, Las Cruces, NM 88003

Received: June 2015

Revised: June 2016

Published: December 2016

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Abstract

The Kirchhoff problem for a neutrally buoyant rigid body dynamically interacting with an ideal fluid is considered. Instead of the standard Kirchhoff equations, equations of motion in which the pressure terms appear explicitly are considered. These equations are shown to satisfy a Hamiltonian constraint formalism, with the pressure playing the role of the Lagrange multiplier. The constraint is imposed on the shape of a compact fluid surface whose dynamics is governed by the canonical variables introduced by Zakharov for a free-surface. It is also shown that the assumption of neutral buoyancy can be relaxed.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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