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Optimal Control for 3D Elastic Body Motions G.V. Kostin, V.V. Saurin The initial-boundary problem for the linear theory of elasticity is considered. Based on the method of integrodifferential relations a new dynamical variational principle in which displacement, stress, and momentum functions are varied is proposed and discussed [1–5]. To minimize the nonnegative functional under initial, boundary, and partial differential constraints arising in this approach a regular algorithm for approximation of the unknown functions is worked out. The algorithm gives us the possibility to estimate explicitly the local and integral quality of obtained numerical solutions. An effective numerical method for the optimization problems of controlled motions of elastic bodies with quadratic objective functionals is developed. As example, the 3D problems of optimal longitudinal motions of a rectilinear elastic prism with a quadratic cross section are considered for the terminal total mechanical energy to be minimized. The numerical results and their error estimates are presented and discussed. References 1. Kostin,G.V., Saurin,V.V.: Modeling of Controlled Motions of an Elastic Rod by the Method of Integro-Differential Relations. J. of Computer and Systems Sciences Int. 45(1), 56–63 (2006) 2. Kostin,G.V., Saurin,V.V.: The Optimization of the Motion of an Elastic Rod by the Method of Integro-Differential Relations. J. of Computer and Systems Sciences Int. 45(2), 217–225 (2006) 3. Kostin,G.V., Saurin,V.V.: Modeling and Optimization of Elastic System Motions by the Method of Integro-Differential Relations. Doklady Mathematics. 73(3), 469–472 (2006) 4. Kostin G.V., Saurin V.V.: The method of integrodifferential relations for linear elasticity problems // Archive of Applied Mechanics. 76(7–8), 391–402 (2006) 5. Kostin G.V., Saurin V.V.: Method of Integro-Differential Relation for Optimal Beam Control. PAMM. Special Issue: GAMM Annual Meeting 2006 – Berlin. 6, (2006) (to print)