You can only have an equilibrium if . and a stable equilibrium if . The last condition is equivalent to: 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:

let with which reduces to earnshaws theorem.

source psfile jl@crush.caltech.edu index

magnet_top_toy