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Differential Equations, Vol. 39, No. 3, 2003, pp. 369–380. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 3, 2003, pp. 343–353. Original Russian Text Copyright c 2003 by Mukharlyamov. ORDINARY DIFFERENTIAL EQUATIONS On the Construction of Di erential Equations of Motion of Constrained Mechanical Systems R. G. Mukharlyamov Friendship of Nations University, Moscow, Russia Received March 11, 2002 INTRODUCTION The dynamics of a constrained mechanical system is described by second-order di erential equa- tions for the generalized coordinates with indeterminate Lagrange multipliers on the right-hand sides. On nding the expressions for the Lagrange multipliers, one obtains a system of di erential equations of motion for which the constraint equations are rst integrals; in the course of numerical solution, the deviations of these rst integrals from the constraint equations grow [1{5]. In the construction of equations of motion, one can treat the constraints imposed on a mechanical system as servo-constraints [6{11], and the constraint reactions can be treated as the corresponding controls. Then the construction of equations of motion can be reduced to nding expressions for the constraint reactions on the right-hand sides guaranteeing that the solutions of the system satisfy the constraint equations with the desired accuracy [12, 13]. This
Differential Equations – Springer Journals
Published: Oct 5, 2004
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