In Classical Mechanics, the state of the system is completely determined by its position and momentum (𝐱(𝑡),𝐩(t)).
Phase space is the space of all (𝐱(𝑡),𝐩(t))
An orbit in phase space corresponds to a system that returns to its initial conditions (e.g. oscillators)pic.twitter.com/GGNH9R1ISl
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Replying to @InertialObservr
When x grows, p should be positive. When x decreases, p should be negative. Am I naive? Maybe this stuff just doesn’t work like that, because of some aspect of quantum mechanics. I don’t know.
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Replying to @oqaqiq @InertialObservr
I’m assuming p=m*dx/dt and maybe that is foolish. I’m not sure.
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Replying to @oqaqiq
If you have an oscillator x= Acos(ωt) and p = -Αωsin(ωt) and so there's no reason in general you would expect x>0 --> p>0
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Replying to @InertialObservr @oqaqiq
If x and p are of that form, should it not trace out an ellipse (not oblique) going clockwise? (x is abscissa, p is ordinate) This way, x is decreasing iff p is negative. I think this is what @opaqiq was pointing out.
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Right, I'm not asserting that this is a standard harmonic oscillator.
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