Hamiltonian in Classical mechanics?

[BiGyElLoWhAt]

I've read a couple of places that a hamiltonian can be a tool used in classical mechanics and that it's eigenvalues are useful pieces of information. I've tried finding info on the subject matter, as I want to see something that actually requires linear algebra, or at least makes good use of it. My linear algebra course kind of sucked to be blunt, and I never really saw much use in it other than some organization.

Can someone hook me up with some links please? I'm probably just not looking up the right things. (I want some sort of instruction, unlike what's on the wikipedia page)

 

[robphy]

Google: "normal modes" "coupled oscillators"

 

[Haborix]

In addition to what robphy suggested, the eigenvalue/eigenvector problem comes up when you study the linear stability of fixed points in phase space. You may have noticed a trend in physics courses to "linearize" systems (wave equations, the linear stability I mentioned, etc.). The reason to do this is so that the problem we have left to solve is a linear algebra problem which is easy (at least relative to the original problem). Don't worry if you can't find linear algebra, it will always find you.