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1. A bidimensional oscillator have energies:
With C and K constants
a) show by a transform of coordinates that this oscillator is equivalent to two isotropic harmonic oscillators.
b) then find two independent constants of motion and verify this using:
with "a" the constant.
I tried to do this problem with a transform of kind
So the Lagrangian is
I wrote the Hamiltonian so in this case represent the energy and this will be a constant of motion, but I can't find the second constant in this problem... I don't Know if the transformation that I used is the correct, or if is another transformation to convert the equivalent problem to two isotropic harmonic oscillators.
I hope you can help me
Thanks
With C and K constants
a) show by a transform of coordinates that this oscillator is equivalent to two isotropic harmonic oscillators.
b) then find two independent constants of motion and verify this using:
with "a" the constant.
I tried to do this problem with a transform of kind
So the Lagrangian is
I wrote the Hamiltonian so in this case represent the energy and this will be a constant of motion, but I can't find the second constant in this problem... I don't Know if the transformation that I used is the correct, or if is another transformation to convert the equivalent problem to two isotropic harmonic oscillators.
I hope you can help me
Thanks