[andrewcooke]

what an awful diagram. it implies there's some kind of symmetry that relates all four, but when you look at the details there are asymmetries. if you think it was helpful look at it again and explain why di appears in two quarants but dq and dv appear once each.

[oofabz]

You can rearrange the inductor equation to get di = (1/L) dϕ. Then the quadrants are perfectly symmetrical except for the ugly 1/L. But that's just an arbitrary unit created by humans, you could fix that by defining the unit of inductance as the inverse of what we use now.

[andrewcooke]

ah, thank-you. that makes more sense.

[dnautics]

are you sure you're looking on both sides of the equations?