Like most things in the military, planning is structured. The planning process is known the MAP – the Military Appreciation Process. It is a systematic and structured process that aims to ensure that all elements have been considered and that a plan meets the test of being feasible, acceptable, suitable and distinguishable enough from other plans to warrant consideration on its own. One of the first steps is to create a Centre of Gravity Construct. This allows the planner to shape a plan to target an opponent's weaknesses. General H. Norman "Stormin'" Norman wrote extensively about it in his autobiography. The Centre of Gravity has a long-winded doctrinal definition, but essentially it is the "thing" that, if you kick it out, will cause your opponent to topple. I have had a quick bash at creating a CoG construct for the first phase of any operation to topple Gaddafi. If the war in Iraq taught us anything, it is that subsequent planning must be focussed on winning the peace as comprehensively as winning the war. This idea, which I bashed out on a slow Saturday night over a couple of beers, is not aimed at a "Phase 2" plan, but at removing a dictator to facilitate a transition into something else. I am not a General, or a politician, or even a planner on a staff HQ. It is just the ousting of Gaddafi according to Sharpe.
Centre of Gravity
Gaddafi's ability to crush dissent and control the population.