December  2016, 8(4): 461-485. doi: 10.3934/jgm.2016016

Kirchhoff's equations of motion via a constrained Zakharov system

1. 

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

Received  June 2015 Revised  June 2016 Published  November 2016

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.
Citation: Banavara N. Shashikanth. Kirchhoff's equations of motion via a constrained Zakharov system. Journal of Geometric Mechanics, 2016, 8 (4) : 461-485. doi: 10.3934/jgm.2016016
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show all references

References:
[1]

volume 75 in series Applied Mathematical Sciences, $2^{nd}$ edition, Springer-Verlag, New York, 1988. doi: 10.1007/978-1-4612-1029-0.  Google Scholar

[2]

Phys. Fluids A, 5 (1993), 3026-3028. doi: 10.1063/1.858712.  Google Scholar

[3]

volume 125 of series Applied Mathematical Sciences, Springer-Verlag, 1998.  Google Scholar

[4]

J. Fluid Mech., 181 (1987), 349-379. doi: 10.1017/S002211208700212X.  Google Scholar

[5]

Reg. Chaotic Dyn., 8 (2003), 449-462. doi: 10.1070/RD2003v008n04ABEH000257.  Google Scholar

[6]

Phys. Rev. Lett., 71 (1993), 1661-1664. doi: 10.1103/PhysRevLett.71.1661.  Google Scholar

[7]

in Proceedings of the Eighth International Workshop on Water Waves and Floating Bodies, 23-26 May 1993, St John's, Newfoundland, Canada, 159-163. Available online from http://www.iwwwfb.org/Abstracts/iwwwfb08/iwwwfb08-41.pdf. Google Scholar

[8]

Second printing of the 1964 original. Belfer Graduate School of Science Monographs Series, 2. Belfer Graduate School of Science, New York; produced and distributed by Academic Press, Inc., New York, 1967.  Google Scholar

[9]

PhD Thesis, University of Vienna, 1904. Google Scholar

[10]

Springer, 2007.  Google Scholar

[11]

Proc. Roy. Soc. Lond. A, 446 (1994), 169-193. doi: 10.1098/rspa.1994.0098.  Google Scholar

[12]

J. Fluid. Mech., 295 (1995), 91-120. doi: 10.1017/S002211209500190X.  Google Scholar

[13]

Cambridge Texts in Applied Mathematics, Cambridge University Press, 1997. doi: 10.1017/CBO9780511624056.  Google Scholar

[14]

Journal für die reine und angewandte Mathematik (Crelle's Journal), 1870 (1870), 237-262. doi: 10.1515/crll.1870.71.237.  Google Scholar

[15]

Physics Letters A, 120 (1987), 391-395. doi: 10.1016/0375-9601(87)90685-2.  Google Scholar

[16]

Soviet Math. Dokl., 26 (1982), 495-498. Google Scholar

[17]

J. Fluid Mech., 1 (1956), 319-336. doi: 10.1017/S0022112056000184.  Google Scholar

[18]

Automatica, 33 (1997), 331-346. doi: 10.1016/S0005-1098(96)00176-8.  Google Scholar

[19]

Physica D, 18 (1986), 391-404. doi: 10.1016/0167-2789(86)90207-1.  Google Scholar

[20]

volume 17 of series Texts in Applied Mathematics, $2^{nd}$ edition, Springer-Verlag, 1999. doi: 10.1007/978-0-387-21792-5.  Google Scholar

[21]

$5^{th}$ edition, Dover, New York, 1996. Google Scholar

[22]

Funktsional Anal. i Prilozhen., 15 (1981), 37-52, Available online from http://www.mi.ras.ru/ snovikov/70.pdf.  Google Scholar

[23]

Funktsional Anal. i Prilozhen, 15 (1981), 54-66, Available online from http://www.mi.ras.ru/ snovikov/69.pdf.  Google Scholar

[24]

Reg. Chaotic Dyn., 7 (2002), 291-298. doi: 10.1070/RD2002v007n03ABEH000211.  Google Scholar

[25]

Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge Univesity Press, 1992.  Google Scholar

[26]

Reg. Chaotic Dyn., 10 (2005), 1-14. doi: 10.1070/RD2005v010n01ABEH000295.  Google Scholar

[27]

Phys. Fluids, 14 (2002), 1214-1227. doi: 10.1063/1.1445183.  Google Scholar

[28]

Theoretical and Computational Fluid Dynamics, 22 (2008), 37-64. doi: 10.1007/s00162-007-0065-y.  Google Scholar

[29]

J. Appl. Mech. Tech. Phys., 9 (1968), 190-194. Originally published in Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi, 9 (1968), 86-94. doi: 10.1007/BF00913182.  Google Scholar

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