Abstract
The nonlinear problem on Watt regulator motion mounted on a machine subjected to set vertical harmonic small-amplitude vibrations is considered. The problem on the existence and stability of the periodic motions of the regulator is investigated by the methods of the classical perturbation theory and the Kolmogorov‒Arnold‒Moser (KAM) theory. Under additional assumptions that the regulated-machine vibrations are high-frequency, an integrable approximate set of equations is obtained and it is shown that the majority of its trajectories are retained also in the complete set.
Similar content being viewed by others
References
D. K. Maxwell, I. A. Vyshnegradskii, and A. Stodola, Theory of Automatic Control (Linearized Problems), Redaction, and Comments of Academician A.A. Andronov and Corresponding Member of AN USSR I.N. Voznesenskii (Izd-vo AN SSSR, Moscow, 1949) [in Russian].
N. E. Zhukowski, Theory of Machine-Motion Control in Collected Works (Gostekhizdat, Leningrad, 1949), Vol. 3, p. 392 [in Russian].
P. Appel’, Theoretical Mechanics (Fizmatgiz, Moscow, 1960), Vol. 2 [in Russian].
S. M. Targ, Brief Course of Theoretical Mechanics (Vysshaya Shkola, Moscow, 2009) [in Russian].
A. M. Zhuravskii, Handbook on Elliptic Functions (Izd-vo AN SSSR, Moscow, 1941) [in Russian].
A. A. Andronov, A. A. Vitt, and S. E. Khaikin, Theory of Vibrations (Fizmatgiz, Leningrad, 1959) [in Russian].
L. S. Pontryagin, Ordinary Differential Equations (NITs “Regular and chaotic dynamics,” Moscow, 2001) [in Russian].
G. E. O. Dzhakal’ya, Methods of the Theory of Perturbations for Nonlinear Sets (Nauka, Moscow, 1979) [in Russian].
V. I. Arnol’d, V. V. Kozlov, and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics (Editorial URSS, Moscow, 2002) [in Russian].
A. P. Markeev, Linear Hamiltonian Sets and Certain Problems on Stability of Motion of Satellite with Respect to Mass Center (NITs “Regular and chaotic dynamics,” Moscow, 2009) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.P. Markeev, 2017, published in Doklady Akademii Nauk, 2017, Vol. 477, No. 4, pp. 415–420.
Rights and permissions
About this article
Cite this article
Markeev, A.P. Watt regulator dynamics. Dokl. Phys. 62, 538–542 (2017). https://doi.org/10.1134/S1028335817120023
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1028335817120023