×

Stability of rotation of a vane in a flow. (English) Zbl 1151.70306

J. Math. Sci., New York 146, No. 3, 5846-5862 (2007); translation from Fundam. Prikl. Mat. 11, No. 7, 73-95 (2005).
Summary: The results of investigation of the stability of permanent rotation of a four-blade vane on a weightless rod in the flow of a homogeneous medium are discussed. The rod rotates about a fixed point where a spherical joint is situated. The vane rotates about the second joint fixed at the other end of the rod. The stability of permanent rotation of the vane is studied when the rod coincides with the dynamic symmetry axis of the vane. The results are compared with the one-joint case. It is shown that increasing the number of degrees of freedom leads to “diminishing” the stability domain projection onto the corresponding subspace of parameters.

MSC:

70E05 Motion of the gyroscope
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] N. G. Chebotaryov and N. N. Meyman, ”Routh-Hurwitz problem for polynomials and integer functions,” Tr. Mat. Inst. Steklov, 26, 1–332 (1949).
[2] O. Flachsbart, ”Messungen an ebenen und gowölbten Platten,” in: L. Prandtl und A. Betz, eds., Ergebnisse der Aerodynamischen Versuchsanstalt zu Göttingen, Bd. 4, München-Berlin (1932), pp. 96–100.
[3] S. V. Guvernyuk, M. P. Falunin, and S. A. Feschenko, ”Investigation of a rotating parachute,” in: O. V. Rysev and M. P. Falunin, eds., Parachutes and Penetrable Bodies (Collected Works Devoted to 70th Anniversary of Acad. Kh. A. Rakhmatullin), Izd. Mosk. Univ., Moscow (1980), pp. 30–44.
[4] I. V. Novozhilov, Fraction Analysis [in Russian], Izd. Mosk. Univ., Moscow (1991). · Zbl 0747.34032
[5] V. A. Privalov, O. G. Privalova, and V. A. Samsonov, ”On the dynamics of a boomerang,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 52–65 (2003).
[6] V. A. Privalov and V. A. Samsonov, ”On the stability of motion of a body autorotating in flow,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 32–38 (1990).
[7] V. A. Privalov and V. A. Samsonov, ”Comparison of stability properties of two autorotation modes,” Prikl. Mat. Mekh., 58, No. 2, 37–48 (1994). · Zbl 0823.70019
[8] V. A. Samsonov, V. A. Privalov, A. N. Zenkin, and T. P. Sokolova, Investigation of Stability of an Autorotating Body, Report of the Institute of Mechanics of MSU, No. 3534 (1987).
[9] V. G. Tabachnikov, ”Standard characteristics of wings for low speeds in the whole range of angle of attack,” Tr. TsAGI, No. 1621, 79–93 (1974).
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.