Literature Cited
F. D. Bairamov, “The technical stability in a system with distributed parameters subject to permanent perturbations,” Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., No. 2, 5–11 (1974).
K. G. Valeev and G. S. Finin, Constructing Lyapunov Functions [in Russian], Naukova Dumka, Kiev (1981).
V. I. Zubov, Lectures on Control Theory [in Russian], Nauka, Moscow (1975).
K. A. Karacharov and A. G. Pilyutik, Introduction to the Technical Theory of Stability of Motion [in Russian], Fizmatgiz, Moscow (1972).
N. F. Kirichenko, Some Aspects of Motion Stability and Controllability [in Russian], Izd. Kiev. Univ., Kiev (1972).
K. S. Matviichuk, “Notes on a comparison method for a differential-equation system with rapidly rotating phase,” Ukr. Mat. Zh.34, No. 4, 456–461 (1982).
K. S. Matviichuk, “A comparison principle for the equations for a system of coupled bodies containing damping elements,” Ukr. Mat. Zh.,34, No. 5, 625–630 (1982).
K. S. Matviichuk, “The technical stability of a coupled system of bodies containing damping elements,” Prikl. Mekh.,19, No. 5, 100–106 (1983).
K. S. Matviichuk, “Existence and stability conditions for solutions to singular Kirkwood-Salzburg integral equations. Parts 1 and 2,” Teor. Mat. Fiz.,49, No. 1, 63–76 (1981).
K. S. Matviichuk, “Existence and stability conditions for solutions to singular Kirkwood-Salzburg integral equations. Part 3,” Teor. Mat. Fiz.,51, No. 1, 86–101 (1982).
K. S. Matviichuk, “A comparison method for differential equations close to hyperbolic,” Differents. Uravn.,20, No. 11, 2009–2011 (1984).
K. S. Matviichuk, “Technical stability in some systems having distributed parameters,” Prikl. Mekh.,21, No. 8, 97–104 (1985).
K. S. Matviichuk, “Technical stability in a nonlinear dynamic system having slow and fast motions,” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 2, 11–15 (1986).
K. S. Matviichuk, “Inequalities for solutions to some nonlinear partial differential equations,” Mat. Fiz. Nelin. Mekh., No. 5 (39), 82–87 (1986).
K. S. Matviichuk, “Technical stability in a parametrically excited distributed process,” Prikl. Mat. Mekh.,50, No. 2, 210–218 (1986).
K. S. Matviichuk, “Stability in a straight pipeline transporting a liquid,” in: Problems in Pipeline Transport for Oil and Gas: Abstracts [in Russian], Ivano-Frankovsk (1985), pp. 220–221.
K. S. Matviichuk, “Stability conditions for nonlinear parametrically excited distributed processes,” Vychisl. Prikl. Mat.,58, 107–112 (1986).
K. S. Matviichuk, “Technical stability for nonlinear parametrically excited distributed processes,” Differents. Uravn.,22, No. 11, 2001–2004 (1986).
A. A. Movchan, “Stability in solid-body deformation,” Arch. Mech. Stosowanej,15, 659–682 (1963).
E. L. Nikolai, Gyroscope Theory [in Russian], Gostekhizdat, Leningrad-Moscow (1948).
Ya. G. Panovko and I. I. Gubanova, Stability and Oscillations in Elastic Systems [in Russian], Nauka, Moscow (1967).
N. P. Plakhtienko, “Determining the natural frequencies of a cantilever bearing a gyroscope,” Prikl. Mekh.,23, No. 2, 160–163 (1987).
T. K. Sirazetdinov, Stability in a System with Distributed Parameters [in Russian], Izd. Kazan. Aviats. Inst., Kazan' (1971).
V. Ya. Skorobagat'ko, Researches on the Qualitative Theory of Partial Differential Equations [in Russian], Naukova Dumka, Kiev (1980).
H. Leipholz, Stability of Elastic Systems, Sijthoff et Noorhoff, Alphen aan den Rijn, The Netherlands (1980).
J. Szarski, Differential Inequalities, PWN, Warsaw (1967).
Additional information
Mechanics Institute, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 5, pp. 96–102, May, 1990.
Rights and permissions
About this article
Cite this article
Matviichuk, K.S. Technical-stability conditions for the rotation of a body on a vertical elastic rod. Soviet Applied Mechanics 26, 505–509 (1990). https://doi.org/10.1007/BF00887271
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00887271