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- Thread starter digogalvao
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What other coordinate is that?notwrite the Hamiltonian as a function of derivatives of the momenta. Second, it is unclear to me what "it" that is supposed to mean that the system has no cyclic coordinates is. What property of the expression are you referring to? Clearly, none of the coordinates that you have are cyclic, but that does not mean that there are necessarily other coordinates you could use where one of them would be cyclic (as in fact there is in this case).

- #4

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What symmetries does the Hamiltonian have? In what coordinates would the Hamiltonian therefore not depend on one of the coordinates?What other coordinate is that?

Hint: What you have is quite clearly a 2-dimensional harmonic oscillator.

- #5

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Yes, the frequency is ##\frac{1}{\sqrt{m}}##. Should I put everything in polar coordinates?What symmetries does the Hamiltonian have? In what coordinates would the Hamiltonian therefore not depend on one of the coordinates?

Hint: What you have is quite clearly a 2-dimensional harmonic oscillator.

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What happens if you do?

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