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Some remarks on the integrability of the equations of motion of a rigid body in an ideal fluid. (English. Russian original) Zbl 0495.70016

Funct. Anal. Appl. 15, 144-146 (1981); translation from Funkts. Anal. Prilozh. 15, No. 2, 83-85 (1981).

MSC:

70E15 Free motion of a rigid body
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
76B99 Incompressible inviscid fluids
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References:

[1] G. Kirchhoff, Vorlesungen über Mathematische Physik, Vol. 1, Mechanik, Teubner, Leipzig (1876). · JFM 08.0542.01
[2] A. Clebsch, Math. Ann.,3, 238-262 (1871). · JFM 02.0733.01 · doi:10.1007/BF01443985
[3] V. Steklov, Math. Ann.,42, 273-294 (1893). · JFM 25.1499.01 · doi:10.1007/BF01444182
[4] A. Liauunoff, Reports of Kharkov Math. Soc., Ser. 2,4, Nos. 1-2, 81-85 (1893); Gesammelte Werke, Vol. 1, pp. 320-324.
[5] G. V. Kolossoff, C. R. Acad. Sci., Paris,169, 685-686 (1919).
[6] J. Moser, ”Various aspects of integrable Hamiltonian systems,” to appear in Proc. CIME conference, held in Bressanone, Italy, June, 1978.
[7] J. Moser, ”Geometry of quadrics and spectral theory,” Preprint, Courant Institute (1979).
[8] S. V. Manakov, Funkts. Anal. Prilozhen.,10, No. 4, 93-94 (1976).
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