23 - jordan23 filled

23 - jordan23 filled - ME 575 Handouts Eigenvectors When...

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ME 575 Handouts 1 ME575 Session 23 – Jordan Canonical Form; Generalized Eigenvectors School of Mechanical Engineering Purdue University Slide 1 Eigenvectors Eigenvectors • When initial conditions align with an When initial conditions align with an eigenvector, the solution stays on that eigenvector, i.e., if the system starts in a given eigenvector, i.e., if the system starts in a given mode, it follows that mode to equilibrium. • Eigenvectors Eigenvectors diagonalize diagonalize the A matrix. the A matrix. ME575 Session 23 – Jordan Canonical Form; Generalized Eigenvectors School of Mechanical Engineering Purdue University Slide 2 Eigenvectors Eigenvectors State vector written in terms of state variables: State vector written in terms of state variables: Represent state vector in terms of eigenvectors: Represent state vector in terms of eigenvectors: ⎤⎡ ⎥⎢ =++ + ⎦⎣ " ## # 12 n 10 0 01 0 xx x x 00 1 + = " n n i x x (assume x 1: unit length)
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ME 575 Handouts 2 ME575 Session 23 – Jordan Canonical Form; Generalized Eigenvectors School of Mechanical Engineering Purdue University
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This note was uploaded on 12/09/2011 for the course ME 575 taught by Professor Meckl during the Fall '10 term at Purdue.

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23 - jordan23 filled - ME 575 Handouts Eigenvectors When...

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