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Math Help - Simple eigen value / vector problem needed

  1. #1
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    Simple eigen value / vector problem needed

    Good evening.

    I am delivering an introductory course on matrices to mechanical engineering students.

    Does anyone know of a simple mechanical problem that can be solved using matrices, preferably by finding eigenvalues and then vectors of a third order matrix?

    Finding vibrational modes in systems is interesting but of too high a level; solving simultaneous equations is too easy. Is there anything in between? I am aware of electrical engineering examples, but these will be a last resort.

    Thanks in advance,

    W
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  2. #2
    A Plied Mathematician
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    How about finding the principal moments of inertia? That essentially allows you to diagonalize the inertia tensor, which enables you to solve problems like the heavy symmetric spinning top, although you don't have to go through with all of that analysis (requires Euler-Lagrange formulation of mechanics).

    Other than that, solving systems of linear ODE's such as you get in linear circuits or mass-spring systems (the vibrational modes you talked about) are still the best examples that I know of.
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