Assume 5 charged particles (charge 1) constrained to live on the surface of a sphere are in a configuration that minimizes electrostatic potential energy. Are there configurations that are stable but that are not the minimum energy configuration? A simple computer program could quickly(?) examine many random configurations and slowly map out the potential energy surface E(θ_1,phi_1,θ_2,phi_2,θ_3,phi_3,θ_4,phi_4,θ_5,phi_5)? There must be more elegant(less computer time) ways to find the minimum energy configuration? Has this problem been solved? Edit, E above is a function of only 8 variables, we can always let one particle be at the north pole? Thanks for any help!