 | | 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
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 37, Issue 2 / 2002 | Next article >> |
| S. V. Volkov, "Control of relative vibrations of a pendulum on a rotating platform," Mech. Solids. 37 (2), 19-27 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
2 |
Pages |
19-27 |
| Title |
Control of relative vibrations of a pendulum on a rotating platform |
| Author(s) |
S. V. Volkov (Moscow) |
| Abstract |
Kinematic equations are compiled for a design relative motion
of two rigid bodies forming a mechanical system with two degrees
of freedom. These equations are utilized for the synthesis
of a feedback control supporting this motion. The properties
of the design motion are specified in terms of a system of differential
equations dot x=y, dot y=Y(x,y) having a prescribed set
of singular trajectories and a prescribed structure of the
entire phase space. The function Y(x,y) belongs to the class C1.
The torque is determined which is applied to the axis of rotation of
the platform and provides the asymptotic stability for the design
vibratory motion of the pendulum mounted on this platform. |
| References |
| 1. | G. V. Korenev, Essays on Mechanics of Purposeful Motion
[in Russian], Nauka, Moscow, 1980. |
| 2. | A. S. Galiullin, Inverse Dynamics Problems [in Russian],
Nauka, Moscow, 1981. |
| 3. | A. S. Galiullin, Methods for Solving Inverse Dynamics Problems [in
Russian], Nauka, Moscow, 1986. |
| 4. | A. S. Galiullin, I. A. Mukhametzyanov, R. G. Mukharlyamov,
and V. D. Furasov, Construction of Equations of Design Motion
for Controlled System [in Russian], Izd-vo UDN, Moscow, 1969. |
| 5. | A. S. Galiullin (Editor), Design Motion of Mechanical Systems
[in Russian], Izd-vo UDN, Moscow, 1971. |
| 6. | A. S. Galiullin, "Construction of equations of motion,"
Differentsial'nye Uravneniya [Differential Equations],
Vol. 12, No. 2, pp. 195-237, 1977. |
| 7. | I. A. Mukhametzyanov and R. G. Mukharlyamov, Equations of Design
Motions [in Russian],
Izd-vo UDN, Moscow, 1986. |
| 8. | I. A. Mukhametzyanov and R. G. Mukharlyamov, Equations of Design
Motion, Optimization, and Estimates [in Russian],
Izd-vo UDN, Moscow, 1986. |
| 9. | N. P. Erugin, "Construction of the whole set of systems of differential
equations having a prescribed integral curve," PMM [Applied Mathematics
and Mechanics], Vol. 16, No. 6, pp. 659-670, 1952. |
| 10. | M. I. Al'mukhamedov, "Inverse problem of the qualitative theory
of differential equations," Izv. Vuzov. Matematika, No. 4, pp. 3-6, 1963. |
| 11. | M. I. Al'mukhamedov, "On the construction of a differential
equation having prescribed curves being its limit cycles," Izv. Vuzov.
Matematika, No. 1, pp. 12-16, 1965. |
| 12. | R. G. Mukharlyamov, "To the inverse problems of the qualitative theory
of differential equations,"
Differentsial'nye Uravneniya [Differential Equations],
Vol. 2, No. 10, pp. 1673-1681, 1967. |
| 13. | S. V. Volkov, Construction of Differential Operators for
Dynamical Systems [in Russian], Izd-vo RUDN, Moscow, 1999. |
| 14. | M. Frommer, "Integral curves of a first-order
ordinary differential equation in the neighborhood of a singular point
having rational character," Uspekhi Matem. Nauk, No. 9,
pp. 212-253, 1941. |
|
| Received |
13 April 2001 |
| << Previous article | Volume 37, Issue 2 / 2002 | Next article >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English