Hamilton's equations of motion

  • Thread starter physics-?
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  • #1
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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 = AT , a symmetric 3-by-3 matrix.
Which force do you obtain?
Is this force conservative?

Thanks!
 

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi physics-?! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
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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!
 
  • #4
tiny-tim
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if A was diagonal, (r,Ar) would be ax2 + by2 + cz2

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

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