I AM NOT ASSERTING THIS IS THE PHASE SPACE ORBIT OF A SIMPLE HARMONIC OSCILLATOR
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This example seems false to me.
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What do you mean?
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why this ellipse is tilted ? 1/2 *k*x^2+p^2/(2*m) = E The above equation can not be tilted ellipse in x & p.
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Phase space is the space of all (𝐱(𝑡),𝐩(t))