electrostatics: E=qU+mgz

You can only have an equilibrium if tex2html_wrap96 . and a stable equilibrium if tex2html_wrap97 . The last condition is equivalent to: tex2html_wrap98 This can be diagonalized. Laplace's equation imples that at least one of the derivatives must be negative, which means things are unstable.

Examples: trojan asteroids around jupiter.

In magnetostatics: tex2html_wrap99

tex2html_wrap100 let tex2html_wrap101 with tex2html_wrap102 which reduces to earnshaws theorem.

source psfile jl@crush.caltech.edu index