Differential Equations Solutions 123

Differential Equations Solutions 123 - Chapter 22 Solutions...

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Chapter 22 Solutions: Case Study: Robot Control: Swinging Like a Pendulum (coauthored by Yalin E. Sagduyu) CHALLENGE 22.1. Under the transformation, equation (1) becomes · 10 cm ± ¸ " y ± (1) ( t ) y ± (2) ( t ) ± = · y (2) ( t ) mg sin( y (1) ( t )) ¸ , or " y ± (1) ( t ) y ± (2) ( t ) ± = · c/ ( )1 / ( ) ¸· y (2) ( t ) mg sin( y (1) ( t )) ¸ . Replacing sin( y (1) ( t )) by y (1) ( t ) gives the system y ± = " y ± (1) ( t ) y ± (2) ( t ) ± = · 01 g/± c/ ( ) y (1) ( t ) y (2) ( t ) ¸ = Ay . The eigenvalues of the matrix A are the roots of det( A λ I ) = 0, or the roots of λ 2 + λc/ ( )+ = 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.

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