hw5_98F - Homework #5, 1998 Fall MEAM 501 1. Analytical...

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MEAM 501 Analytical Methods in Mechanics and Mechanical Engineering 1. Consider a constrained minimization problem ( 29 ( 29 n n n n T T K F F R b R A R v b v Av v v v v - = × , , , 2 1 , min { } m n m n K R g R B 0 g Bv R v - = × , , : where a matrix A is symmetric, that is, A A = T , and the constrained set K is non- empty. (1) Find the necessary condition that an element K u is a minimizer of the functional F on the constrained set K . (2) Obtain the Lagrangian L to this constrained minimization problem, and set up the "equivalent" unconstrained problem on the primal variable v by considering the necessary condition of the problem obtained by the Lagrange multiplier method. (3) Solve the problem for A , B , and g defined as follows : - - - - - - - - - - - - - - - - - - = 2 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 2 1 0 0 0 0 0 0 0 0 1 2
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hw5_98F - Homework #5, 1998 Fall MEAM 501 1. Analytical...

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