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IssuesArchive of Issues2011-4pp.534-543

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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
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