Perelomov, A. M. 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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 15 Documents 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 Keywords:motion of rigid body in ideal fluid; equations for geodesics; right- invariant metric; six-parameter Lie group E(3); Clebsch case; L-M pair for n-dimensional generalization of Clebsch case; L-M pair of Moser; additional quadratic integral of motion; Steklov cases Citations:Zbl 0343.70003; Zbl 0455.58018 PDFBibTeX XMLCite \textit{A. M. Perelomov}, Funct. Anal. Appl. 15, 144--146 (1981; Zbl 0495.70016); translation from Funkts. Anal. Prilozh. 15, No. 2, 83--85 (1981) Full Text: DOI 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). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.