 | | 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
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 46, Issue 4 / 2011 | Next article >> |
| R.G. Mukharlyamov, "Differential-Algebraic Equations of Programmed Motions of Lagrangian Dynamical Systems," Mech. Solids. 46 (4), 534-543 (2011) |
| Year |
2011 |
Volume |
46 |
Number |
4 |
Pages |
534-543 |
| DOI |
10.3103/S0025654411040042 |
| Title |
Differential-Algebraic Equations of Programmed Motions of Lagrangian Dynamical Systems |
| Author(s) |
R.G. Mukharlyamov (Peoples' Friendship University of Russia, Miklukho-Maklaya 6, Moscow, 117198 Russia, rmuharliamov@sci.pfu.edu.ru) |
| Abstract |
We suggest a method for constructing the dynamic equations of manipulator systems in canonical variables. The system of differential dynamic equations has an integral manifold corresponding to the holonomic and nonholonomic constraint
equations. The controls are determined so as to ensure the stability of this manifold. We state conditions for the exponential stability of the manifold and for constraint stabilization when solving the dynamic equations numerically by a simplest difference method. We also present the solution of the problem of control of a plane two-link manipulator. |
| Keywords |
equations of dynamics, programmed constraint, constraint stabilization, system, stability, canonical variables, perturbation, numerical solution |
| References |
| 1. | R. P. Paul,
Modelling, Trajectory Calculation, and Servoing of a Computer Controller Manipulator
(Nauka, Moscow, 1976)
[Russian translation]. |
| 2. | F. L. Chernous'ko, N. N. Bolotnik, and V. G. Gradetskii,
Manipulation Robots: Dynamics, Control, and Optimization
(Nauka, Moscow, 1989)
[in Russian]. |
| 3. | R. G. Mukharlyamov,
"Control of Program Motion of Multilink Manipulators,"
Vestnik RUDN. Ser. Prikl. Mat. Inf.
No. 1, 22-39 (1998). |
| 4. | R. G. Mukharlyamov,
"Stabilization of the Motions of Mechanical Systems in Prescribed Phase-Space Manifolds,"
Prikl. Mat. Mekh.
70 (2), 236-249 (2006)
[J. Appl. Math. Mech. (Engl. Transl.)
70 (2), 210-222 (2006)]. |
| 5. | A. P. Markeev,
Libration Points in Celestial Mechanics and Space Dynamics
(Nauka, Moscow, 1978)
[in Russian]. |
| 6. | V. G. Vilke,
Theoretical Mechanics
(Izd-vo MGU, Moscow, 1998)
[in Russian]. |
| 7. | W. D. MacMillan,
Dynamics of Rigid Bodies
(New York, London, 1936; Izd-vo Inostr. Lit., Moscow, 1951). |
| 8. | N. A. Kilchevskii, N. I. Remizova, and E. N. Kilchevskaya,
Foundations of Theoretical Mechanics
(Vishcha Shkola, Kiev, 1986)
[in Russian]. |
| 9. | R. A. Layton,
Principles of Analytical System Dynamics
(Springer, New York, 1998). |
| 10. | R. G. Mukharlyamov,
"On the Construction of the Set of Systems of Differential Equations of Stable Motions
over an Integral Manifold,"
Differents. Uravn.
5 (4), 688-699 (1969)
[Differ. Equations (Engl. Transl.)]. |
|
| Received |
25 December 2008 |
| Link to Fulltext |
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