Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear Algebra for Coupled Oscillators

  1. Jan 9, 2013 #1
    Hi guys, first post!

    I'm doing some side work on coupled oscillating systems, and I've almost found a procedure to get the analytic solution (an n-dimentional vector function of time) to a mass-spring system in which n masses are arraigned in a line and separated by springs, but I need help solving this equation for D. I'm asking a pure math question here, you can ignore all the above if you like.

    D and F are diagonal.
    S is a sparse symmetric matrix.
    I think that N is invertible.
    All the matrices are square nxn.


    Solving D on either side seems pointless because you can't isolate it (as far as I can see).

    DNF=SDN ---> D=SDNF-1N-1
    DNF=SDN ---> S-1DNFN-1=D

    Can I simplify NF-1N-1 in the first line or NFN-1 in the second, using the fact that F and its inverse are diagonal? Obviously I can't. But can you?

    I tried taking the transpose of both sides of the original equation and using the fact that the transpose of a symmetric matrix is itself:


    So now I have two equations, the second derived from the first and making use of what I see to be everything we know in general about these matrices:


    Any suggestions on where to go from here?

  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Linear Algebra for Coupled Oscillators
  1. Linear Algebra (Replies: 1)

  2. Linear algebra (Replies: 2)

  3. Linear algebra (Replies: 2)