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Prog. Theor. Phys. Vol. 124 No. 3 (2010) pp. 517-531

[ Full Text PDF : OPEN SELECT (161K) ]

Clebsch Potentials in the Variational Principle for a Perfect Fluid

Hiroki Fukagawa1,* and Youhei Fujitani1,2,**

1School of Fundamental Science & Technology, Keio University, Yokohama 223-8522, Japan
2Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan

(Received January 4, 2010; Revised June 30, 2010)

Abstract:

Equations for a perfect fluid can be obtained by means of the variational principle both in the Lagrangian description and in the Eulerian one. It is known that we need additional fields somehow to describe a rotational isentropic flow in the latter description. We give a simple explanation for these fields; they are introduced to fix both ends of a pathline in the variational calculus. This restriction is imposed in the former description, and should be imposed in the latter description. It is also shown that we can derive a canonical Hamiltonian formulation for a perfect fluid by regarding the velocity field as the input in the framework of control theory.

Subject Index : 518, 519
URL : http://ptp.ipap.jp/link?PTP/124/517/
DOI : 10.1143/PTP.124.517


*E-mail: hiroki@beer.appi.keio.ac.jp
**E-mail: youhei@appi.keio.ac.jp

[ Full Text PDF : OPEN SELECT (161K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 127 No. 5 (2012) pp. 921-935 :
    A Variational Principle for Dissipative Fluid Dynamics
    Hiroki Fukagawa and Youhei Fujitani

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