Abstract
We present a survey of the principal results obtained by V. N. Koshlyakov in analytical mechanics, dynamics of solids, and applied theory of gyroscopes.
Similar content being viewed by others
References
V. N. Koshlyakov, “On the deviations of the gyrovertical for variable velocity of proper rotation of the rotor of a gyroscope,” Inzh. Sb. Akad. Nauk SSSR, 6, 185–196 (1950).
V. N. Koshlyakov, “On several, special cases of integration of the Euler dynamical equations related to the motion of a gyroscope in a resisting medium,” Prikl. Mat. Mekh., 17, No. 2, 137–148 (1953).
V. N. Koshlyakov, Theory of Gyrocompasses [in Russian], Nauka, Moscow (1972).
V. N. Koshlyakov, “On the theory of, gyrocompasses,” Prikl. Mat. Mekh., 23, No. 5, 810–817 (1959).
V. N. Koshlyakov, “On the asymptotic solution of equations of motion of a gyrocompass,” Prikl. Mat. Mekh., 24, No. 5, 790–795 (1960).
V. N. Koshlyakov, “On the reducibility of equations of motion of a gyrohorizon compass,” Prikl Mat. Mekh., 25, No. 5, 801–805 (1961).
V. N. Koshlyakov, “On the stability of a gyrohorizon compass in the presence of dissipative forces,” Prikl. Mat. Mekh., 26, No. 3 412–417 (1962).
V. N. Koshlyakov and V. F. Lyashenko, “On one integral in the theory of gyrohorizon compasses,” Prikl. Mat. Mekh., 27, No. 1, 10–15 (1963).
V. N. Koshlyakov and V. F. Lyashenko, “On the stability of gyrocompasses,” Prikl. Mat. Mekh., 28, No. 5, 885–887 (1964).
V. N. Koshlyakov and S. P. Sosnitskii, “On the stability of gyrocompasses,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 3, 32–35 (1969).
V. N. Koshlyakov, “On the stability of two-rotor gyrocompasses of pendulum type,” in: Navigation and Control over the Motion of Mechanical Systems [in Russian], Instiute of Mathematics, Ukrainian Academy of Sciences, Kiev (1980), pp. 3–8.
V. N. Koshlyakov, “On the theory of gyrocompasses in the light of analogy with stability of elastic systems,” in: Mechanics of Gyroscopic Systems [in Russian], Kiev Polytechnic Institute, Kiev (1981), pp. 3–11.
V. N. Koshlyakov, “On the theory of stability of nonconservative systems,” in: Navigation and Control [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1982), pp. 3–10.
V. P. Vasilenko, A. N. Kostritsa, and V. N. Koshlyakov, “On the theory of one-rotor adjustable gyrocompasses,” Mekh. Tverd. Tela, 2, 38–46 (1967).
V. N. Koshlyakov, “Problems of the Dynamics of a Solid Body in the Applied Theory of Gyroscopes [in Russian], Nauka, Moscow (1985).
V. N. Koshlyakov, “On equations of location of a moving object,” Prikl. Mat. Mekh., 28, No. 6, 1135–1137 (1964).
V. N. Koshlyakov, “On the application of the Rodrigues-Hamilton and Cayley-Klein parameters in the applied theory of gyroscopes,” Prikl. Mat. Mekh., 29, No. 4, 729–733 (1965).
V. N. Koshlyakov, “On the problem of construction of a certain class of solutions of a gyropendulum system,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 32–38 (1975).
V. N. Koshlyakov, “The Magnus problem in the Rodrigues-Hamilton parameters,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 4, 40–44 (1984).
V. N. Koshlyakov, “Application of the Rodrigues-Hamilton parameters in the Magnus problem,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 2, 43–48 (1985).
V. N. Koshlyakov, “The generalized Magnus formula,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 8, 6–9 (1985).
V. N. Koshlyakov, “On equations of motion of a heavy solid body about a fixed point,” Ukr. Mat. Zh., 25, No. 5, 677–681 (1973).
V. N. Koshlyakov, “On the application of the Rodrigues-Hamilton and Cayley-Klein parameters in the problem of motion of a heavy solid body about a fixed point,” Ukr. Mat. Zh. 26, No. 2, 179–187 (1974).
V. N. Koshlyakov, “On the equations of a gyrostat in the Rodrigues-Hamilton parameters,” Ukr. Mat. Zh., 26, No. 5, 657–663 (1974).
V. N. Koshlyakov, “Equations of a heavy solid body that rotates about a fixed point in unitary and Hermitian matrices,” Ukr. Mat. Zh., 33, No. 1, 9–16 (1981).
V. N. Koshlyakov, “On the equations of a heavy solid body that rotates about a fixed point in the Rodrigues-Hamilton parameters,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 16–25 (1983).
V. N. Koshlyakov, “On one modification of the Lagrange gyroscope,” in: Systems of Navigation and Control [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1983), 3–9.
V. N. Koshlyakov, “On the application of the Rodrigues-Hamilton parameters to the problem of motion of a heavy solid body about a fixed point,” in: Application of Methods of the Theory of Nonlinear Oscillations in Mechanics, Physics, Electrical Engineering, and Biology [in Russian], Naukova Dumka, Kiev (1984), pp. 145–150.
V. N. Koshlyakov and E. S. Bogulavskaya,” On the equations of motion of a heavy solid body in the Rodrigues-Hamilton parameters,” in: Systems of Course Indication and Inertial Navigation [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1985), pp. 3–9.
V. N. Koshlyakov, “On one case of instability of rapid rotation of a body about the vertical,” in: Adjustable Navigational Systems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986), pp. 37–44.
V. N. Koshlyakov, “Rodrigues-Hamilton parameters in problems, of dynamics of solid bodies and applied theory of gyroscopes,” in Mechanics and Progress in Science, and Technology Vol. 1. General and Applied Mechanics [in Russian], Nauka, Moscow (1987). pp. 117–127.
V. N. Koshlyakov, “On equations of motion of a heavy solid body in the Rodrigues-Hamilton parameters,” Ukr. Mat. Zh., 40, No. 2, 182–192 (1988).
V. N. Koshlyakov, “On one case of instability of a rapidly rotating heavy solid body,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 4, 45–50 (1988).
V. N. Koshlyakov, “On the instability of vertical rotation of a heavy body,” Ukr. Mat. Zh., 41, No. 9, 1214–1221 (1989).
V. N. Koshlyakov, “Generalized Euler equations in the Rodrigues-Hamilton parameters,” in: Stability and Control in Mechanical Systems [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 21–26.
V. N. Koshlyakov, “On one effect of instability in the motion of a rapidly rotating body near the vertical,” Izv. Ros. Akad. Nauk, Mekh. Tverd. Tela, No. 1, 10–19 (1993).
V. N. Koshlyakov, “Generalized Euler equations in quaternion components,” Ukr. Mat. Zh., 46, No. 10, 1414–1417 (1994).
V. N. Koshlyakov, “On the reduction of the order of equations of motion of a heavy body near the vertical,” Izv. Ros. Akad. Nauk, Mekh. Tverd., Tela, No 4, 3–7 (1996).
V. N. Koshlyakov, “Rodrigues-Hamilton Parameters and Their Application in Mechanics of Solid Bodies [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992).
V. N. Koshlyakov, “On structural transformations of equations of perturbed motion of one class of dynamical systems” Ukr. Mat. Zh., 49, No. 4, 535–539 (1994).
V. N. Koshlyakov, “On the stability of motion of a symmetric body installed on a vibrating base,” Ukr. Mat. Zh., 47, No. 12, 1661–1666 (1995).
V. N. Koshlyakov, “A Concise Course in Theoretical Mechanics [in Russian], Vyshcha Shkola, Kiev (1993).
Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 11, pp. 1444–1453, November, 1977.
Rights and permissions
About this article
Cite this article
Mitropl’s’kii, Y.A., Samoilenko, A.M., Kalinovich, V.N. et al. On V.N. Koshlyakov’s works in mechanics and its applications. Ukr Math J 49, 1622–1631 (1997). https://doi.org/10.1007/BF02487501
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487501