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The center of the cube is equally unstable along all axes.
Although there is a conservation law for "lines of force"
(which have to do [with] equilibrium, not stability), there is
no corresponding conservation law for "lines of stability".
"... and will have opposite stability on the axis."
Please help me here.
One (J.D.) has suggested derivative zeroes (higher order zeros). If I read it
correctly, they don't necessarily indicate stability -- "convex" away from the
zero(s). Zeros at the bottom of a concavity would be stable, right?