Some problems of rigid body dynamics and their application to the theory of crushers
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Abstract
In this paper we consider the motion of a system consisting of three rigid bodies rotating around a fixed point and having a common axis of own rotation. The chosen system gives a schematic diagram of the working part of a crusher of the Mekhanobr type. Differential equations of motion of a rigid body rotating around a fixed point were derived for the first time, as is known, by L. Euler, who also pointed out one of the cases when the solution under any initial conditions is reduced to quadrature. Further fundamental results in this matter were obtained by Lagrange, S. V. Kovalevskaya, A. M. Lyapunov and others.
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(Archived) Without section
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References
- Krylov A. N. and Krutkov Yu. A. General theory of gyroscopes and some technical applications. Izd. AN SSSR, 1932. (in Russian)
- Bulgakov B. V. Applied theory of gyroscopes. GITTL, 1955. (in Russian)
- Kudrevich B. I. Theory and Practice of Gyroscopic Compass. Izd. Gidrogr. upr., pt. II‑III, 1931, 1933. (in Russian)
- Okunev B. N. Free motion of a gyroscope. GITTL, 1951. (in Russian)
- Klein F. und Sommerfeld A. Uber die Theorie des Kreisels. Hefte 1, 2, 3, 4, Leipzig, 1910, 1914, 1918, 1922.
- Ferri E. S. Applied gyrodynamics. ONTI, 1936. (in Russian)
- Grammel R. The gyroscope, its theory and applications. V. I, 11, IL, 1952. (in Russian)
- Blekhman I. I. Dynamics of a gyroscopic crusher of the system of D. K. Cherkasov. Manuscript. Fondy instituta Mekhanobr, 1952 (report No. 6317). (in Russian)
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