Chapter 22Solutions: Case Study:Robot Control: SwingingLike a Pendulum(coauthored by Yalin E. Sagduyu)CHALLENGE 22.1.Under the transformation, equation (1) becomes·10cm±¸"y±(1)(t)y±(2)(t)±=·y(2)(t)−mgsin(y(1)(t))¸,or"y±(1)(t)y±(2)(t)±=·−c/(m±)1/(m±)¸·y(2)(t)−mgsin(y(1)(t))¸.Replacing sin(y(1)(t)) byy(1)(t) gives the systemy±="y±(1)(t)y±(2)(t)±=·01−g/±−c/(m±)y(1)(t)y(2)(t)¸=Ay.The eigenvalues of the matrixAare the roots of det(A−λI) = 0, or the roots ofλ2+λc/(m±)+= 0, and these are
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.