What Are Hamilton's Equations of Motion for a Quadratic Potential?

[physics-?]

Having a bit of trouble with this question, if anyone could help?

For the following questions we assume the Hamiltonian to
be of the generic form
H(r, p) = T(p) + V (r) = p²/2m+ V(r)
where T(p) and V (r) denote kinetic and potential energies, respectively.
Find Hamilton's equations of motion for a general quadratic potential V (r) = [(r,Ar)]/2
A = A^T , a symmetric 3-by-3 matrix.
Which force do you obtain?
Is this force conservative?

Thanks!

 

[tiny-tim]

welcome to pf!

hi physics-?! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[physics-?]

Well if I'm honest I don't really know where to begin!
I am having trouble understanding it.
Sorry that's not much use to you!

 

[tiny-tim]

if A was diagonal, (r,Ar) would be ax² + by² + cz²

the off-diagonal elements add some xy and yz and zx to that