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I’m assuming p=m*dx/dt and maybe that is foolish. I’m not sure.
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
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.
Right, I'm not asserting that this is a standard harmonic oscillator.
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Phase space is the space of all (𝐱(𝑡),𝐩(t))
