 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| In English (Mech. Solids): | | 4810 |
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| A.P. Markeev, "On Splitting of Separatrices Corresponding to the Operating Mode of the Watt Governor," Mech. Solids. 58 (8), 2731-2737 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
8 |
Pages |
2731-2737 |
| DOI |
10.3103/S0025654423080137 |
| Title |
On Splitting of Separatrices Corresponding to the Operating Mode of the Watt Governor |
| Author(s) |
A.P. Markeev (Moscow Aviation Institute (National Research University), Moscow, 125993 Russia, anat-markeev@mail.ru) |
| Abstract |
The nonlinear problem of the Watt governor dynamics is investigated. It is assumed to be
installed on a machine that performs specified harmonic vibrations of small amplitude along the vertical. Viscous friction forces are assumed to arise in regulator hinges of the, and these forces are small.
In the main operating mode of the regulator, its rods, carrying massive weights, are deflected from the
downward vertical by a constant acute angle. If friction and vertical vibrations of the machine are
neglected, an approximate problem is obtained in which the regulator dynamics is described by an
autonomous Hamiltonian system with one degree of freedom. On the phase portrait of the approximate problem, the operating mode corresponds to a singular point of the center type. The trajectories
encircling this point lie inside the separatrix, which is a homoclinic doubly asymptotic trajectory that
passes through the equilibrium position corresponding to the vertical position of the rods with weights.
In the phase portrait, this position corresponds to a saddle singular point. The Melnikov method is
used to obtain the splitting condition for the unperturbed separatrix in the complete perturbed problem, taking into account dissipation in the hinges and vertical vibrations of the machine. |
| Keywords |
Watt governor, separatrix splitting, chaotic motion |
| Received |
22 May 2023 | Revised |
15 July 2023 | Accepted |
20 July 2023 |
| Link to Fulltext |
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